Boris Johnson said he wanted to “change the country for the better” after he became the UK’s new prime minister.
Speaking outside No 10, he said Brexit would happen on 31 October “no ifs, no buts”, adding “the buck stops here”.
“The doubters, the doomsters, the gloomsters” who said it could not be done were “wrong”, the new PM added.
Mr Johnson is making sweeping changes to his top team. Leadership rival Jeremy Hunt is among more than a dozen ministers to have quit or been sacked.
Announcing his departure, the foreign secretary said he had been offered an alternative role but had turned it down.
Defence Secretary Penny Mordaunt, a leading Brexiteer who is popular across the party, was one of the more surprising sackings.
Another prominent Brexiteer, International Trade Secretary Liam Fox, was also ousted, along with Business Secretary Greg Clark – a vocal opponent of a no-deal Brexit.
All three supported Mr Hunt in the Tory leadership contest.
Education Secretary Damian Hinds, Northern Ireland Secretary Karen Bradley, Immigration Minister Caroline Nokes and Communities Secretary James Brokenshire have also gone, along with Chris Grayling, whose record as Transport Secretary was much criticised.
Scottish Secretary David Mundell, who has left his position after four years, joked whether there would be “room” on the backbenches after all the dismissals.
This comes on top of the earlier resignations of four leading ministers, including Chancellor Philip Hammond, Justice Secretary David Gauke and Cabinet Office minister David Lidington.
Conservative MP Nigel Evans described the changes as a “summer’s day massacre”.
The BBC’s chief political correspondent Vicki Young said the sackings suggested Mr Johnson wasn’t looking to build bridges across the party.
Instead, she said, he was focused above all else on assembling the team he thought would bring about the results he needed, even if that was controversial.
Sajid Javid, who has been tipped to take the vacant role of chancellor of the exchequer, has entered Downing Street.
So too have Priti Patel – a former international development secretary – and Dominic Raab – a former Brexit secretary. Both have been vocal backers of Mr Johnson.
Earlier in a 13-minute speech outside Downing Street, Mr Johnson listed a wide range of domestic ambitions, chiefly a promise to sort out care for the elderly “once and for all”.
Reforms to the social care sector have eluded previous governments because of their cost and complexity.
“We will fix it once and for all with a clear plan we have prepared to give every older person the dignity and security they deserve,” he insisted.
Mr Johnson also pledged to improve infrastructure, recruit 20,000 new police officers and “level up” school spending. He promised reforms to ensure the £20bn in extra funding earmarked for the NHS “really gets to the front line”.
And he pledged to boost the UK’s biotech and space science sectors, change the tax rules to provide incentives for investment, and do more to promote the welfare of animals.
Setting out his priorities for office, the former London mayor hit out at the “pessimists” who did not believe Brexit could be delivered and called for an end to three years of indecision.
“The people who bet against Britain are going to lose their shirts because we are going to restore trust in our democracy,” he said.
“The time has come to act, to take decisions and change this country for the better.”
He said he had “every confidence” the UK would leave the EU in 99 days time with a deal, but preparations for the “remote possibility” of a no-deal Brexit would be accelerated.
Mr Johnson vowed to bring all four nations of the United Kingdom – or what he described as the “awesome foursome” – together in the task of strengthening a post-Brexit country.
“Though I am today building a great team of men and women, I will take personal responsibility for the change I want to see,” he concluded.
“Never mind the backstop, the buck stops here.”
The BBC’s Vicki Young said she was struck by the ambition of Mr Johnson’s objectives beyond Brexit and the fact that he would take personal responsibility for his success or failure in achieving them.
Labour’s Sir Keir Starmer said Mr Johnson’s speech was “all rhetoric” and the new PM needed to show leadership rather than the “glib” answers he had become known for.
The new Lib Dem leader, Jo Swinson, said she would welcome a cross-party push to find a solution on social care, but attacked Mr Johnson’s “bluster and bravado” over Brexit.
Mr Johnson took over after Theresa May handed in her resignation to the Queen. A number of her senior ministers have also already resigned, saying they could not serve under her successor.
Earlier, as she relinquished power after three years, Mrs May said being prime minister had been “the greatest honour” and wished her successor well.
During his journey to Buckingham Palace, his car was briefly held up by protesters from Greenpeace, who formed a human chain across The Mall.
Mr Johnson’s partner, Carrie Symonds, and key members of his staff were awaiting the new prime minister’s arrival in Downing Street.