Michael Gove has been sacked from the government as Prime Minister Theresa May puts together her new team, in her first full day in Downing Street.
Education Secretary Nicky Morgan has also gone, as well as Culture Secretary John Whittingdale.
Brexit campaigner Boris Johnson said he was “humbled” having been named new foreign secretary, in a surprise move.
Philip Hammond became chancellor, Amber Rudd is home secretary, and Eurosceptic David Davis is new Brexit secretary.
Asked about his first priorities as chancellor, Mr Hammond said there would be “no emergency Budget”.
He said he would work closely with the Bank of England and other economic experts and make “carefully considered decisions over the summer”, followed by an Autumn Statement “in the normal way”.
Before the EU referendum, his predecessor George Osborne said he would have to cut public spending and increase taxes in an emergency Budget if the UK voted for Brexit.
Mrs May has told European leaders she is committed to the UK leaving the EU.
In a series of congratulatory phone calls taken by Mrs May on Wednesday evening, the UK’s second female prime minister spoke to German Chancellor Angela Merkel, French President Francois Hollande and Irish Taoiseach Enda Kenny.
A Downing Street spokesman said the new prime minister had “emphasised her commitment to delivering the will of the British people to leave the European Union”.
“The prime minister explained that we would need some time to prepare for these negotiations and spoke of her hope that these could be conducted in a constructive and positive spirit,” the spokesman added.
Mrs May will continue to fill out her new cabinet later on Thursday, with the new secretaries of state for health, education, and work and pensions among those expected to be appointed.
Mrs May began forming her new cabinet shortly after her arrival into 10 Downing Street.
Her first cabinet announcement was former foreign secretary Mr Hammond as chancellor – replacing Mr Osborne.
Mr Osborne had been fired because his “brand” was seen as “too tarnished”, BBC political editor Laura Kuenssberg said.
But in a move that surprised the political world, Mrs May put Mr Johnson – one of the most prominent figures of the campaign to leave the EU – in charge of the Foreign and Commonwealth Office.
Mr Johnson , who has said he is “very humbled” and “very proud” at the appointment, is no stranger to controversy – or gaffes – on the international stage.
During the EU referendum campaign, he drew criticism for comments he made about US President Barack Obama who he said had an “ancestral dislike” of the UK because of his “part-Kenyan” heritage.
In 2015, Mr Johnson had to cancel planned public events in the West Bank because of security fears after he criticised backers of a boycott on Israeli goods, and he has previously described Hilary Clinton – US presidential hopeful – as having “a steely blue stare, like a sadistic nurse in a mental hospital”.
The cabinet appointment throws Mr Johnson a lifeline after a turbulent couple of weeks which saw his Tory leadership bid torpedoed by Justice Secretary and fellow Brexit campaigner Michael Gove.
On Wednesday, Mr Johnson told the BBC: “Clearly now we have a massive opportunity in this country to make a great success of our relationship with Europe and with the world and I’m very excited to be asked to play a part in that.”
However, Liberal Democrat leader Tim Farron predicted the new foreign secretary would “spend more time apologising to nations he’s offended” than carrying out the job.
Asked for his view of Mr Johnson’s appointment, Mr Hammond told BBC Radio 4’s Today: “We’ve got a range of different characters and a range of different styles and a range of different talents.”
The chancellor also told Today the UK economy was entering “a new phase” because of the vote to leave the EU, which he said had had a “chilling” short-term effect on the economy.
“It has shaken confidence and caused many businesses to pause investment decisions that they were making,” he said.
He said the government now needed to “send signals of reassurance about the future as quickly and as powerful as we can”.
The chancellor also said he believed in the need to reduce the deficit further, but that the government must look again at “how and at when and at what pace”, in the light of the new circumstances faced by the economy.
Mrs May also appointed Liam Fox to the new position of secretary of state for international trade, while Michael Fallon was retained as defence secretary.
Speaking to reporters outside his home on Thursday morning Mr Fox said there were “tremendous opportunities” to increase the UK’s global profile, adding: “We should be extraordinarily optimistic and confident about the future.”
After visiting Buckingham Palace, where she was formally appointed as prime minister by the Queen, Mrs May made her first speech outside 10 Downing Street.
She vowed to lead a government that worked for all, not just the “privileged few”, promising to give people who were “just managing” and “working around the clock” more control over their lives.
For an “ordinary working class family”, she added, “life is much harder than many people in Westminster realise”.
She highlighted the “precious bond” between England, Scotland, Wales and Northern Ireland and between “every one of us”.
Mrs May also paid tribute to her predecessor David Cameron, saying he had been “a great modern prime minister”.
Mr Cameron had earlier given his final speech as prime minister outside Number 10, saying the job had been “the greatest honour” of his life and that the UK was “much stronger” than when he took over.
He took part in his final Prime Minister’s Questions in the House of Commons, where he was given a standing ovation by Conservative MPs, before formally tendering his resignation to the Queen.