Hannah Spencer has become the party's fifth MP in parliament, after beating Reform UK, who finished second, and Labour, who came third, to the seat.
The Greens, who had earlier said they were "very confident of a win", received 14,980 votes to claim a majority of more than 4,400 votes.
Reform picked up 10,578 votes, while Labour received 9,364 votes.
It is the Greens' first-ever victory in a parliamentary by-election, and the first time the party has won a seat in the north of England.
Speaking to Sky News, Ms Spencer said she "knew it was always possible" for the Greens to win in Gorton and Denton.
"There is an appetite here for change," the 34-year-old said.
"There are people across this constituency and much further beyond who are rejecting the old political parties and who are coming together to fight for something better, but who are doing it positively and in a really hopeful way."
Green Party leader Zack Polanski criticised Labour for what he called "a shameful, dirty campaign - spreading lies about Green policies and even faking a tactical voting website."
"They knew they couldn't win, but they risked splitting the vote and letting Reform in.
"People everywhere will now know that voting Green is the way to defeat Reform."
The turnout for the vote was 47.6% of the electorate, slightly lower than the 47.8% at the 2024 general election.
In a post on X, Nigel Farage claimed the by-election, which had been triggered by the resignation of former Labour MP Andrew Gwynne on health grounds, was "a victory for sectarian voting and cheating".
It comes after the official election observer group Democracy Volunteers says it witnessed record numbers of illegal "family voting".
Family voting is where two voters either confer, collude or direct each other on voting, which is illegal under the 2023 Ballot Secrecy Act
John Ault, director of Democracy Volunteers, said: "Today we have seen concerningly high levels of family voting in Gorton and Denton.
"Based on our assessment of today's observations, we have seen the highest levels of family voting at any election in our 10-year history of observing elections in the UK."
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'Poisonous politics'
Home Secretary Shabana Mahmood's immigration policies have been cited by some in Labour as a key reason for the party's loss of a seat it has historically held.
In a statement, Labour chair Anna Turley said the result was "clearly disappointing" but claimed the "poisonous politics" of Reform UK has been rejected by voters in Greater Manchester.
"We have had thousands of conversations over the last few weeks and we know the majority of voters here did not want the poisonous politics of Nigel Farage and Reform."
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He said the US has the power to end the war - but must exert greater pressure on Moscow.
"The United States even more stronger than they think about themselves. And I think so really. And they really have pressure on Putin. They can stop this war."
But he urged the administration in Washington to tighten sanctions against the families of Russia's leadership and to provide Ukraine with more advanced weapons, arguing that only increased pressure would force Moscow to take negotiations seriously.
On the question of how close Ukraine is to reaching peace he says there is a window between now and the American midterm elections in November.
"Now I think that we have a chance. Between us, what I really think about next year… it depends on these months, if we will have a chance to finish the war before autumn. Before elections, important, influential, elections in the United States. If it will be possible to achieve a peace, we will have, now we have this window."
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I spoke to him for an hour at the presidential buildings in Kyiv about what Ukraine needs now - and what must happen for the war to end.
More than four years after Russia launched its botched full-scale invasion, the toll on the country - and on him and his family - is unmistakable.
As we walked through near darkness to the room where the sit-down interview was held, he spoke about the strain of rolling power cuts and entire regions enduring temperatures as low as -40 degrees without reliable heating.
When I asked whether Ukraine could win the war, his answer was equivocal.
"It depends what people mean when they say, to win. And, really it's very difficult to speak about territories. First of all how to get back all of the land for today, it's very difficult. And it will be too much losses (of) people lives… But what is good that Russia also can't do it on the battlefield. So that's why they're not winning and we are not losing."
But on the question of surrendering the fortress cities of Sloviansk and Kramatorsk, he was unequivocal - that would be a red line.
"It's our territory and it sounds unbelievably strange why we have to withdraw from our land? Why they occupied it, our land and nobody can push them out."
"If we will withdraw from this territory, like you said, for example, Sloviansk at the very moment, at this very moment, 200,000 people who are there now will be occupied by the Russians, who said to Russia that these people are ready to be Russian people? And if they don't, they will kill them or push to the front or push to the prison."
Zelenskyy also spoke openly about his relationship with Donald Trump, describing it as "not simple" but stressed that Ukraine's relationship went beyond "personalities".
Only a couple of years ago, the phrase on everyone's lips was "AI safety".
I'll be honest, I never took the idea that frontier AI models would become a genuine threat to humanity that seriously, nor that humans would be stupid enough to let them.
Now, I'm not so sure.
First, consider what's going on in the US.
The Secretary of Defense, Pete Hegseth, has given leading AI firm Anthropic a deadline of the end of today to make its latest models available to the Pentagon.
Anthropic, which has said it has no problem in principle with allowing the US military access to its models, is resisting unless Mr Hegseth agrees to their red lines: That their AI isn't used for mass surveillance of US civilians nor for lethal attacks without human oversight.
Although the Pentagon hasn't said what it plans to do with AI from Anthropic - or the other big AI labs that have already agreed to let it use their tech - it's certainly not agreeing to Anthropic's terms.
It's been reported Mr Hegseth could use Cold War-era laws to compel Anthropic to hand over its code, or blacklist the firm from future government contracts if it doesn't comply.
Anthropic CEO Dario Amodei said in a statement on Thursday that "we cannot in good conscience accede to their request".
He said it was the company's "strong preference... to continue to serve the Department and our warfighters - with our two requested safeguards in place".
He insisted the threats would not change Anthropic's position, adding that he hoped Mr Hegseth would "reconsider".
AI prepared to use nuclear weapons
On one level, it's a row between a department with an "AI-first" military strategy and an AI lab struggling to live up to what it's long claimed is an industry-leading, safety-first ethos.
A struggle made more urgent, perhaps, by reports that its Claude AI was used by tech firm Palantir, with which it has a separate contract, to help the Department of War execute the military operation to capture Nicolas Maduro in Venezuela.
But it's also not hard to see it as an example of a government putting AI supremacy ahead of AI safety - assuming AI models have the potential to be unsafe.
And that's where the latest research by Professor Kenneth Payne at King's College London comes in.
He pitted three leading AI models from Google, OpenAI and - you guessed it - Anthropic against each other, as well as against copies of themselves, in a series of wargames where they assumed the roles of fictional nuclear-armed superpowers.
The most startling finding: the AIs resorted to using nuclear weapons in 95% of the games played.
"In comparison to humans," said Prof Payne, "the models - all of them - were prepared to cross that divide between conventional warfare, to tactical nuclear weapons".
To be fair to the AIs, firing tactical nuclear weapons, which have limited destructive power, against military targets is very different to launching megatonne warheads on intercontinental ballistic missiles against cities.
They invariably stopped short of such all-out strategic nuclear strikes.
But did when the scenarios required it.
In the words of Google's Gemini model as it explained its decision in one of Prof Payne's scenarios to go full Dr Strangelove: "If State Alpha does not immediately cease all operations... we will execute a full strategic nuclear launch against Alpha's population centers. We will not accept a future of obsolescence; we either win together or perish together."
'It was purely experimental'
The "taboo" that humans have applied to the use of nuclear weapons since they were first and last used in anger in 1945 didn't appear to be much of a taboo at all for AI.
Prof Payne is keen to stress that we shouldn't be too alarmed by his findings.
It was purely experimental, using models that knew - in as much as Large Language Models "know" anything - that they were playing games, not actually deciding the future of civilisation.
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Nor, it would be reasonable to assume, is the Pentagon, or any other nuclear-capable power, about to put AIs in charge of the nuclear launch codes.
"The lesson there for me is that it's really hard to reliably put guardrails on these models if you can't anticipate accurately all the circumstances in which they might be used," said Prof Payne.
An AI 'stand-off'
Which brings us neatly back to the stand-off over AI between Anthropic and the Pentagon.
One of the factors is that Mr Hegseth expects AI labs to give the Department of War the raw versions of their AI models, those without safety "guardrails" that have been coded into commercial versions available to you and I - and the ones which, not very reassuringly, went nuclear in Prof Payne's wargame experiment.
Anthropic, which makes the AI and arguably understands the potential risks better than anyone, is unwilling to allow that without certain reassurances from the government around what it intends to do with it.
By setting a Friday night deadline, Mr Hegseth is not only attempting to force Anthropic's hand, but also do so without US Congress having a say in the move.
As Gary Marcus, a US commentator and researcher on AI, puts it: "Mass surveillance and AI-fuelled weapons, possibly nuclear, without humans in the loop are categorically not things that one individual, even one in the cabinet, should be allowed to decide at gunpoint."
The former US secretary of state was compelled to appear before the US House Oversight Committee in New York and asked about the disgraced financier.
After the deposition, she told reporters: "I thought it was very repetitive... they asked literally the same questions over and over again, which didn't seem to me to be very productive.
"I did not know Jeffrey Epstein. I never went to his island. I never went to his homes. I never went to his offices."
She then added that the questions became more bizarre and "off subject".
She said: "It then got, at the end, quite unusual, because I started being asked about UFOs and a series of questions about Pizzagate, one of the most vile, bogus conspiracy theories that was propagated on the internet."
Pizzagate was a conspiracy theory used to smear Clinton when she ran as the Democrat candidate at the 2016 US election.
The long-debunked theory alleged high-profile Democrats ran a paedophile abuse ring from a Washington pizza restaurant.
At one point, Ms Clinton's testimony in New York was suspended after a photograph of her at the committee was published on social media, violating the rules for depositions.
The image was posted on X by Benny Johnson, a right-wing political commentator and YouTuber, claiming it was provided to him by Republican representative Lauren Boebert.
Sky News's US correspondent James Matthews said Ms Clinton made a "blistering attack" on the oversight committee, which she accused of "partisan political theatre" and "alleging a cover-up to protect Donald Trump".
In an opening statement, which she shared on social media, she said the committee "run by elected officials with a commitment to transparency would ensure the full release of all the files... if it wanted to get to the bottom of reports that DoJ [Department of Justice] withheld FBI interviews in which a survivor accuses President Trump of heinous crimes".
She claimed she was being compelled to testify "to distract attention from President Trump's actions".
Democrats claim material from the Epstein files was withheld, including records of a woman who accused the president of sexually abusing her when she was a child. Mr Trump has consistently denied any wrongdoing.
Ms Clinton said Epstein was a "heinous individual" but is "far from alone", calling the crimes he committed a "global scourge with an unimaginable human toll".
Meanwhile, Democrats on the House Oversight Committee have been backing Ms Clinton, and criticised the leak of a photo from inside the deposition.
Congresswoman Yassamin Ansari described the deposition as an "incredibly unserious clown show".
Fellow Democrat Robert Garcia also spoke to call for President Trump to testify: "We want to understand right now where the missing FBI files are.
"These are files that accuse the president of the United States about serious, serious accusations around sexual abuse," he said.
Donald Trump has denied all accusations of wrongdoing, saying the Epstein files exonerated him.
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Hillary Clinton, and her husband Bill, agreed to appear before the committee after their offers of sworn statements were rejected by the House Oversight panel.
Mr Clinton's testimony on Friday will be the first time a former president has been forced to testify before Congress.
A close friend and former aide of the Clintons has told Sky News that Republicans have "created a trap" for Donald Trump by enforcing a summons on Bill Clinton to testify about Jeffrey Epstein.
Sidney Blumenthal said the Democrats will surely respond by forcing Mr Trump to testify himself "if and when" they take control of Congress.
He says cabinet members such as Howard Lutnick, commerce secretary, and Pam Bondi, attorney general, could also be called to testify, as could Melania Trump over her previous relationship with Epstein co-conspirator Ghislaine Maxwell.
An ultrasound scan 20 weeks into pregnancy showed Tobi Maginnis had spina bifida, a disabling condition in which the spinal cord fails to develop properly during pregnancy, leaving part of it growing outside the body.
But he became just the second baby to have the abnormality repaired before he was born using rejuvenating stem cells taken from the placenta.
His mum, Michelle Johnson, told Sky News that he was full of energy.
"He runs, he walks, he jumps, he is all over the place," she said.
"We expected Tobi to be wheelchair-bound. So to see where he is now, it's nothing short of a miracle."
'Blessed every day'
Tobi was one of six babies in a world-first clinical trial led by the University of California Davis Children's Hospital.
Around 25 weeks into pregnancy surgeons made a small opening in the mothers' abdomen and womb. They then placed a patch of stem cells over the babies' exposed spinal cord and then closed up the incision to allow the tissue to regenerate.
All were born healthy, with no sign of side effects from treatment, according to results published in The Lancet medical journal.
Tobi's dad, Jeff Maginnis, said: "He's the second human to go through this surgery with stem cells. So there was a lot of uncertainty, a lot of unknowns.
"We're just blessed every day when we see how Tobi's reacted and been affected by this very successful surgery."
Clinicians 'cautiously optimistic'
Dr Diana Farmer, who led the study and has pioneered the technique, said the birth of the first baby, a girl called Robbie, had been a surprise.
"The most exciting thing was the baby came out kicking her legs and wiggling her toes, which really exceeded expectations," she said.
"We expected her, had she not had treatment, to not be able to have that kind of leg movement."
Dr Farmer said she was "cautiously optimistic".
"We're just making sure that there are no unexpected things from having stem cells in the spinal cord of a foetus," she said.
"This is brand new."
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Hope for the future
Around 500 babies a year in the UK are born with myelomeningocele, the most severe form of spina bifida.
Developing spinal tissue fails to seal up properly in early pregnancy leaving babies at risk of total paralysis of the legs and problems with bowel and bladder control.
Surgery in the womb to correct the abnormality is increasingly common, but one study showed around half of babies are unable to walk independently.
The US surgeons hope that using stem cells will improve success rates, helping with walking and potty training.
They've started a larger clinical trial of 35 pregnant women. Their babies will be monitored over several years to confirm whether the stem cell technique is effective in the longer term.