Dominic Raab and Priti Patel return to government as foreign secretary and home secretary respectively.
Sajid Javid has been named as the new chancellor as more than half of Theresa May's old cabinet, including leadership rival Jeremy Hunt, quit or were sacked.
Earlier, Mr Johnson said the Brexit "doomsters and gloomsters" were wrong and the UK would leave on 31 October.
Speaking outside No 10, he said the UK would meet that deadline "no ifs, no buts", adding: "The buck stops with me."
Mr Johnson then turned his attention to a radical overhaul of the government, with 17 of Mrs May's former senior ministers being axed or stepping down.
Announcing his departure, Foreign Secretary Mr Hunt 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 the most surprising departure. She has been replaced by Ben Wallace, a former soldier and longstanding ally of Mr Johnson's.
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, Culture Secretary Jeremy Wright and Communities Secretary James Brokenshire have also gone, along with Chris Grayling, whose record as Transport Secretary was much criticised.
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.
Former Home Secretary Sajid Javid - a banker before entering politics - has been given the key role of chancellor, having thrown his weight behind Boris Johnson after being eliminated from the leadership race himself.
Priti Patel - who quit as international development secretary in 2017 after holding unauthorised meetings with Israeli officials - succeeds Mr Javid at the Home Office, where she said she would focus on keeping the UK country safe and fighting "the scourge of crime".
Dominic Raab is a former Brexit secretary, but quit over Mrs May's handling of the process.
He said he was "hugely humbled" by his appointment and said the UK needed to "bring finality" to Brexit so it could focus on the other big challenges.
In other moves, Michael Gove leaves behind his environment brief to become Chancellor of the Duchy of Lancaster, while Steve Barclay has been re-appointed as Brexit Secretary.
More about: BorisJohnson
