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 player telling French referee Francois Letexier that he had been targeted.
The match was stopped for 11 minutes and Vinicius, who is black, 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 has repeatedly suffered racism in Spain during games.
Player 'could be banned' if found guilty
The match was eventually resumed with the first leg ending 1-0. The teams are due to go to Madrid to play the second leg, 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, Vinicius Junior's team-mate 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."
In exercises in one of the world's most strategic waterways, it left little doubt of its capabilities with missile strikes on dummy targets and simulated tanker seizures.
Supreme Leader Ayatollah Ali Khamenei wasn't mincing his words either.
"A warship is a dangerous device," he said. "But more dangerous than that is a weapon that can send that warship deep under the sea."
A fifth of the world's oil supply passes through the Strait of Hormuz, and Iran's exercises have closed it, albeit temporarily, giving a clear sense of what could be to come if the US strikes Iran.
Just a few hundred miles east, a formidable array of US military forces is also amassing.
Read more: Iran and US agree 'guiding principles' after talks
The USS Lincoln aircraft carrier strike group has been conducting exercises of its own. The kind you only carry out if you are preparing for offensive action.
A stretch of water the world relies on for 20% of its oil is becoming cluttered with rival navies, both drilling for war. What could possibly go wrong?
So, what are the chances of diplomacy averting the chances of conflict?
Iran's foreign minister, Abbas Araghchi, emerged from talks sounding hopeful. He's optimistic that the basis for future negotiations has been laid, but warned that an agreement could still be a long way off.
A seasoned diplomat and veteran of negotiations with the West, he cannot afford to look obstructive. The Iranians will want to play for time.
US President Donald Trump has said failure to do a deal could lead to strikes on Iran.
Read more:
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But the Iranians say a deal on the terms that Trump is currently proposing would be tantamount to surrender. Giving up its nuclear enrichment completely is a red line. Trump says it's a prerequisite.
Squaring that, and many other circles, will be fiendishly difficult.
Without progress, the region is undoubtedly moving closer to war.
The shooting happened at the Dennis M. Lynch Arena in Pawtucket, near Providence, Rhode Island, at around 2.30pm local time on Monday, where a youth hockey game was due to take place.
Robert Dorgan, 56, killed two people - ex-wife Rhonda and adult son Aidan - and critically injured three others, according to police. Those injured have been identified as Ms Dorgan's parents and a family friend, Pawtucket Police chief Tina Goncalves said.
Dorgan, who was also known as Roberta Esposito, then died from an apparent self-inflicted gunshot wound, Ms Goncalves added.
The police chief said Dorgan's attack was cut short by an unnamed "Good Samaritan" among the spectators, who intervened and brought the shooting "to a swift end".
Players and spectators raced for cover after popping sounds were heard at the venue, according to unverified footage published on social media, which also showed a man throwing himself at Dorgan to stop the shooting.
Ms Goncalves said at least three bystanders were able to contain Dorgan, who reached for a second gun and shot themselves.
Authorities believe the attack stemmed from a "family dispute", but there was "no indication" that there would be violence at the ice rink on Monday, Ms Goncalves said, adding that Dorgan had been to many hockey games before without incident.
Tearful families and high school hockey players still in their kits could be seen hugging outside the arena after the shooting, while police cordoned off the ice rink.
One of the shooting victims was found dead inside the arena, while the other died in hospital, where the three others who suffered gunshot injuries remain in critical condition.
The attack comes almost two months after a gunman killed three people after opening fire at Brown University, in nearby Providence, before turning his weapon on himself.
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"Our state is grieving again," Rhode Island Governor Dan McKee said in a statement. "As governor, a parent, and a former coach, my heart breaks for the victims, families, students, and everyone impacted by the devastating shooting at Lynch Arena in Pawtucket."