Mr Obama has credited the civil rights leader, who died on Tuesday aged 84, with laying the foundation for his own successful presidential run, and said that he and his wife, Michelle, "stand on his shoulders".
The pair were long time friends and associates, with Reverend Jackson endorsing Mr Obama for both of his presidential campaigns.
In a statement shared to social media, Mr Obama said: "Michelle and I were deeply saddened to hear about the passing of a true giant, the Rev Jesse Jackson.
"For more than 60 years, Reverend Jackson helped lead some of the most significant movements for change in human history.
"From organising boycotts and sit-ins, to registering millions of voters, to advocating for freedom and democracy around the world, he was relentless in his belief that we are all children of God, deserving of dignity and respect.
"Reverend Jackson also created opportunities for generations of African Americans and inspired countless more, including us.
"Michelle got her first glimpse of political organizing at the Jacksons' kitchen table when she was a teenager.
"And in his two historic runs for president, he laid the foundation for my own campaign to the highest office of the land.
"Michelle and I will always be grateful for Jesse's lifetime of service, and the friendship our families share.
"We stood on his shoulders. We send our deepest condolences to the Jackson family, and everyone in Chicago and beyond who knew and loved him."
US presidents of all political stripes have paid tribute to Rev Jackson, who himself ran for the Democratic presidential nomination on two occasions.
"Reverend Jackson never stopped working for a better America with brighter tomorrows," wrote Bill and Hilary Clinton in a joint statement.
They added that their "dear friend" had "championed the concerns of Black, Latino, Asian and lower-income white Americans".
In 2000, Mr Clinton awarded Rev Jackson the Presidential Medal of Freedom, the nation's highest civilian honour.
Joe Biden also described Jackson as a "man of God and of the people".
He went on to thank the civil rights leader for his "lifetime of dedicated service and inspirational leadership".
Meanwhile, US President Donald Trump posted a tribute to his Truth Social platform.
He described Jackson as a "a good man, with lots of personality, grit, and 'street smarts'".
Mr Trump continued: "Despite the fact that I am falsely and consistently called a Racist by the Scoundrels and Lunatics on the Radical Left, Democrats ALL, it was always my pleasure to help Jesse along the way."
He also took a swipe at Mr Obama, claiming that Rev Jackson had "much to do" his election, but was not acknowledged or given credit.
Mr Trump added that Rev Jackson "could not stand" Mr Obama.
Born in Greenville, North Carolina, the son of a single, teenage mother, Rev Jackson grew up in a deeply segregated southern community.
He went on to become one of the leading figures in the civil rights movement, and was even pictured with Reverend Martin Luther King the day before he was killed.
Rev King's daughter, Bernice, shared an image of the pair to social media alongside the caption: "Both now ancestors".
Civil rights activist Reverend Al Sharpton said: "He was a consequential and transformative leader who changed this nation and the world. He shaped public policy and changed laws.
"He kept the dream alive, and taught young children from broken homes, like me, that we don't have broken spirits."
Tributes also came in from politicians and leading figures on this side of the pond.
Deputy Prime Minister David Lammy described Jackson as a "pillar of the civil rights movement".
He also shared a story about how Jackson had called him after the 2011 riots to offer support.
Hackney North and Stoke Newington MP Diane Abbott shared a picture of the pair after she was first elected in 1987.
The Mother of the House said: "He was very smart, warm and hugely charismatic."
Sky News' Trevor Phillips also shared a touching tribute, in which he said Jackson's "sheer audacity made change beyond just civil rights".
Former prime minister Gordon Brown last week called for UK police to "urgently" re-examine claims women or girls were trafficked to the country aboard flights.
In an article for the New Statesman, Mr Brown said the recently published files relating to Jeffrey Epstein showed the paedophile financier's jet making 90 flights to or from UK airports, including 15 after his 2008 sex offence conviction.
A spokesperson for Essex Police said: "We are assessing the information that has emerged in relation to private flights into and out of Stansted Airport following the publication of the US DoJ [Department of Justice] Epstein files."
Stansted Airport said: "All private aircraft at London Stansted operate through independent Fixed Base Operators, which handle all aspects of private and corporate aviation in line with regulatory requirements. All immigration and customs checks for passengers arriving on private aircraft are carried out directly by Border Force.
"They use entirely independent terminals not operated by London Stansted and no private jet passengers enter the main airport terminal. The airport does not manage or have any visibility of passenger arrangements on privately operated aircraft."
Mr Brown also said that information in the Epstein files suggested "a number of British girls were on 90 Epstein flights organised from UK airports on what was called his [Epstein's] 'Lolita Express'".
The former politician demanded a full inquiry and wrote: "I have asked the Met urgently to re-examine their decision-making in their investigation and the subsequent reviews."
He claimed the files showed in "graphic detail" how Epstein was flying "in girls from Latvia, Lithuania and Russia" to Stansted, where "women were transferred from one Epstein plane to another", adding they "would not need British visas".
He said it also seemed as though UK authorities "never knew what was happening" and "had little or no idea who was being trafficked through our country".
Read more from Sky News:
How did Jeffrey Epstein get rich?
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The statement from Essex Police comes after the National Police Chiefs' Council (NPCC) said that a national group had been set up to support UK police forces, which are "assessing allegations" following the publication of the Epstein files.
A spokesperson for the NPCC said: "A national coordination group has been set up to support a small number of forces assessing allegations that have emerged following the publication of the US DoJ Epstein files."
Earlier this month, Thames Valley Police confirmed it was assessing claims Andrew Mountbatten-Windsor shared confidential reports from his role as the UK's trade envoy with Jeffrey Epstein.
The claims being examined by Thames Valley Police are separate from the assessment of flights by Essex Police.
Andrew has previously denied any wrongdoing over his Epstein links, but has not directly responded to the latest allegations. Being named in the files does not suggest wrongdoing.
The match in Lisbon, Portugal, was halted five minutes into the second half, shortly after Vinicius gave the away side a 1-0 lead in the first leg of the knockout playoffs.
Cameras picked up the 25-year-old telling French referee Francois Letexier he had been targeted.
The match was stopped for 11 minutes and Vinicius went to the sidelines at the Estadio da Luz.
Both coaches, Benfica's Jose Mourinho and Madrid's Alvaro Arbeloa, talked to him at one point.
It appears Benfica players were not happy with the forward because he celebrated his goal by dancing in front of the corner flag, and some went to confront him.
Vinicius had been shown a yellow card after the celebration.
After the complaint, Letexier responded by crossing his arms in front of his face, activating FIFA's anti-racism protocol and stopping the match.
Real's players threatened to leave the pitch as tensions rose, but the referee eventually allowed the match to resume.
Vinicius: Racists are cowards
Vinicius has repeatedly suffered racism in Spain during games. In a message on Instagram after the match, he said: "Nothing that happened here today was new in my life and my family's."
"Racists are, above all, cowards," he added.
"They need to put their shirts over their mouths to demonstrate how weak they are.
"But they have, on their side, the protection of others who, theoretically, have the obligation to punish."
He described the protocol enforced by the referee as serving "no purpose", and said he didn't understand why he was booked for his celebration.
"I don't like appearing in situations like this, even more so after a great victory and when the headlines have to be about Real Madrid, but it's necessary," he said.
Player 'could be banned' if found guilty
The teams are due to go to Madrid to play the second leg, with the Spanish side 1-0 up, but Sky News' sports correspondent Rob Harris said there could be sanctions.
"There can be a ban for the player, if he's found guilty of the racial abuse of Vinicius," he explained.
"Vinicius himself had warned about facing racism in the past, particularly in Spain... and had said that he would be prepared to walk off... if he faced abuse.
"Football often talks about sending out a message, and imposing those bans, to hopefully try to stamp out the scourge of racism. But how often are we still talking about this in football?"
'It's disgusting,' says England star
After the game, teammate Trent Alexander-Arnold, a former Liverpool and England player, told Amazon Prime: "What's happened tonight is a disgrace to football. It's overshadowed the performance, especially after such an amazing goal.
"Vini has been subjected to this a few times throughout his career, there's no place for it in football or society. It's disgusting."
Almost 80% of private prescriptions are for female patients, according to a survey by The Health Foundation, while the highest uptake by age group across both genders are those aged 30 to 49.
It also showed people in the most deprived areas were around a third less likely to be getting the jabs than those in the least deprived, despite the former having far higher obesity levels.
People in poorer areas also tend to start treatment when they are heavier - another sign of inequality.
The data covered 113,630 people who accessed the drugs privately between November 2024 and October 2024.
Read more: What are the available weight loss jabs?
It comes as the NHS works on a phased rollout of Mounjaro, which will take 12 years.
Some 220,000 patients have been prioritised for the first three years. Those eligible for treatment on the NHS have included those with a body mass index over 40 and illnesses such as high blood pressure and type 2 diabetes.
The vast majority of people taking the jabs in the UK are paying for them privately - and recent research suggests those who take them may need to do so for life.
An NHS spokesperson said it was right those "in the greatest clinical need" were prioritised for treatment, and it was "exploring ways to accelerate the offering so that eligible people can benefit from safe and effective treatment wherever they live in England".
More from Sky News:
Obama leads Jesse Jackson tributes
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Samantha Field, from The Health Foundation, warned: "With an estimated 2.4 million people in the UK already prescribed weight loss medications, our findings reveal a stark divide."
With access to the drugs far from equal, she said it's "more important than ever" that the government focuses on preventable measures like healthy eating.
A ban on junk food adverts covering soft drinks, chocolate and even some porridges came into force last month.
The Health Foundation's survey was carried out with online weight management provider Voy.
Rob Jones, the NCA's director of general operations, said online groups had resulted in offenders' behaviour being "rationalised", as "like-minded" abusers are brought together by algorithms.
While they are collaborating on the dark web, they are using mainstream social media as "discovery" platforms to "identify and abuse vulnerable children".
And with youngsters increasingly reliant on the internet themselves, they are at even greater risk.
Mr Jones described the situation as "incredibly damaging", and warned: "We want society to push back and people to confront their offending - that is the opposite of what happens in the online world."
The amount of material referred to the authorities by the National Centre for Missing and Exploited Children has roughly doubled over the past three years, according to the NCA.
Arrests have risen from between 500 and 800 per month a few years ago to 1,000.
During a single week in January, the NCA and forces across the UK made 252 arrests, including 118 people who were then charged. Another 35 people were sentenced in court and 407 children were safeguarded.
Offences that are becoming more prevalent include abusers paying on demand for the abuse of children to be livestreamed - sometimes for as little as £20.
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The NCA also warned of "Com groups" - sadistic groups that gamify abuse which were recently highlighted by a special report from Sky News.
Mr Jones said members of these communities "egg each other on" to commit "even more horrendous crimes".
Tech companies must 'act with urgency'
Becky Riggs, the National Police Chiefs' lead for child protection and abuse investigation, said officers were working "relentlessly" to target abusers.
But she said tech firms must "act with urgency to make their platforms hostile environments for offenders".
Parents, guardians, carers, and teachers should also learn the signs that a child is being abused.
"The trusted adults around them [...] need clear, accessible guidance so they can recognise the signs of harm, have open conversations, and know where to turn for help," Ms Riggs added.
The NCA's warning comes after the government announced a sweeping crackdown on tech companies to protect children from illegal content.
It will include measures to eliminate "vile illegal content created by AI", and could even open the door to an Australia-style age limit on social media, a Number 10 spokesperson said.