Mr Sunak reappointed the trio after culling nearly a dozen of Liz Truss’s top-tier ministers.
Chancellor of the Exchequer Mr Hunt admitted his job would be “tough” as Downing Street announced he would be staying on.
He replaced Kwasi Kwarteng in October and was tasked with stabilising the economy after the mini-budget sent the country into financial chaos.
No 10 also announced that Suella Braveman would return as home secretary. Just under a week ago, Ms Braverman said she had breached a security protocol and consequently resigned from the role.
Grant Shapps, who had replaced Ms Braverman as home secretary, was appointed as business secretary on Tuesday.
Also returning to the cabinet is Dominic Raab. Mr Sunak appointed him as deputy prime minister and justice secretary – roles he previously held under Boris Johnson.
James Cleverly and Ben Wallace will continue on as foreign secretary and defence secretary respectively, having filled these positions during Ms Truss’s premiership.
Following his reappointment, Mr Wallace was adamant that spending on Britain’s armed forces must rise in the face of the growing threat from countries like Russia and China.
Mr Wallace successfully secured commitments to increase the defence budget under both Boris Johnson and Liz Truss.
Meanwhile, Michael Gove returned to the cabinet as levelling up secretary after being dramatically sacked by Mr Johnson in July.
Steve Barclay, who supported both of Mr Sunak’s bids for the Tory leadership, became health secretary, returning to the role he lost under Ms Truss. Ms Truss had given it to Therese Coffey, one of her close confidants.
Others handed back their previous posts were Kemi Badenoch, the trade secretary, and Michelle Donelan, the culture secretary.
Therese Coffey, one of Ms Truss’s closest friends in Westminster, was demoted from deputy prime minister and health secretary to become environment secretary
Penny Mordaunt, left, came out of the reshuffle as Commons Leader, failing to win a promotion after she challenged Mr Sunak for the leadership.
Kit Malthouse resigned from the education secretary role and praised those he worked with in the Department for Education. His replacement, Gillian Keegan, became the fifth education secretary in just under four months as part of the reshuffle.
In her time as an education minister, she was criticised after sharing photographs of herself in France as the A-Level results drama under Gavin Williamson unfolded.
Sir Gavin also returns to government as a minister without portfolio in the Cabinet Office.
Nadhim Zahawi was given minister without portfolio and Conservative Party Chair. During the most recent leadership contest, Mr Zahawi publicly backed Mr Johnson, before switching allegiance to Mr Sunak.
Mark Harper is the new transport secretary taking over from Anne-Marie Trevelyan, while Victoria Prentis was appointed as attorney general.
Tom Tugendhat, who ran in the Tory leadership race triggered by Mr Johnson’s resignation in July has been re-appointed as security minister and will attend cabinet, Downing Street confirmed.
Simon Hart has become the new chief whip – a role that made headlines this month after Mr Hart’s successor, Wendy Morton, resigned then unresigned amid allegations of bullying. Ms Morton stepped down, once again, on Tuesday afternoon.
Several members of Liz Truss’ cabinet, including justice secretary Brandon Lewis and business secretary Jacob Rees-Mogg, announced their resignations prior to the reshuffle.
Mr Lewis posted his resignation letter on Twitter, saying that while he congratulated the new prime minister on a chance to “reunite and rebuild”, he would be stepping down from the front benches after five years in cabinet.
Chloe Smith, the secretary of state for work and pensions, also announced her departure.
The MP for Norwich North, who backed Mr Sunak in the Tory leadership contest, said in a Twitter post that she will support the PM from the backbenches and continue to work hard for her Norwich North constituents.
Former levelling up secretary Simon Clarke said it “has been a great privilege” to serve in cabinet, after resigning from his post.
Ranil Jayawardena also left his post as environment secretary to make way for Ms Coffey.
Robert Buckland said he is leaving as Welsh secretary at his request. In a post on Twitter he said he would support the prime minister from the backbenches.
His is replaced by David TC Davies.
Johnny Mercer, another Sunak supporter, will return to the role of veterans’ affairs minister, Downing Street said. His reappointment comes after he was sacked by Ms Truss who he says laughed at him by delivering the news.
His wife Felicity Cornelius-Mercer later called Ms Truss an “imbecile”, posting a picture mocking the former prime minister as a character from The Muppets television show.
Jake Berry also said he has left his position as Conservative Party chairman.
Earlier on Tuesday as Mr Sunak made his first speech as prime minister outside No10, he warned the nation is facing a “profound economic crisis” as he pledged to fix the “mistakes” of Liz Truss’s leadership.
The freshly-appointed Conservative leader braced the nation for “difficult decisions to come” as he made his first speech after meeting the King.
Mr Sunak, 42, is the UK’s first British-Asian PM and is the youngest keyholder to No 10 for more than 200 years.
He was appointed prime minister by the King after Charles accepted the resignation of Ms Truss after just 49 days in office, making her the shortest-serving leader in history.
In his speech from Downing Street, Mr Sunak said it was “only right to explain why I’m standing here as your new prime minister”, saying: “Right now our country is facing a profound economic crisis.”
He said it is the lingering aftermath of the coronavirus pandemic and Vladimir Putin’s destabilising war in Ukraine.
Mr Sunak said Ms Truss was “not wrong” to want to drive up growth, describing it as a “noble aim”.
He added: “But some mistakes were made. Not born of ill-will or bad intentions – quite the opposite in fact. But mistakes nonetheless.
“I’ve been elected as leader of my party and your prime minister in part to fix them – and that work begins immediately.”
He vowed to place “economic stability and confidence at the heart of this government’s agenda”, after the financial chaos triggered by Ms Truss.
“This will mean difficult decisions to come,” he said, but he promised to repeat the “compassion” he showed during the coronavirus pandemic.