Johnson made his mark on cabinet within hours of outgoing May making her final speech as leader in Parliament, before handing over power to her successor.
Former chief Brexit negotiator Dominic Raab will be Britain’s new foreign secretary while another staunch “Brexiteer”, Priti Patel, will be home secretary, Downing Street said.
Johnson also made former home secretary Sajid Javid chancellor of the exchequer.
Pro-EU former chancellor Philip Hammond, who had vowed not to work with Johnson, resigned earlier on Wednesday.
Javid tweeted that he was “deeply honoured” by his new appointment.
“Looking forward to working with (at)hmtreasury to prepare for leaving the EU, unifying our country and priming our economy for the incredible opportunities that lie ahead,” he wrote.
Liz Truss, who was appointed new international trade secretary, said Johnson had made three “excellent appointments for the Great Offices of State”.
Javid, Patel and Raab are all “modern, positive, free-enterprise Conservatives”, Truss tweeted.
Eurosceptic Raab, who resigned from May’s government in opposition to her Brexit plan, tweeted earlier on Wednesday that Johnson had “set out a far-reaching and aspirational vision and agenda – brimming with optimism”.
Johnson also handed his old friend and former leadership rival Michael Gove the post of minister for the Cabinet Office, which normally deputises for the prime minister.
Brexit Secretary Stephen Barclay will continue in his post, while Ben Wallace is promoted from security minister to defence minister, Downing Street said.
Foreign Secretary Jeremy Hunt, Johnson’s losing rival in the Conservative run-off ballot to succeed May, said he would step down after declining Johnson’s offer of a different post.
At least a dozen other senior ministers left the government on Wednesday.
Earlier, MPs gave outgoing May a standing ovation as they applauded her out of the House of Commons chamber after her final, at times emotional, appearance as leader.
May, 62, appeared to be fighting back tears as she left, stopping to shake hands with the Speaker, John Bercow, on her way out.
“Later today, I will return to the back benches and it will be my first time in 21 years so it is going to be quite a change,” May told MPs as her final weekly question session in parliament came to a close.
Praising the link between MPs and the constituents they represent as “the bedrock of our parliamentary democracy”, May’s voice quivered as she finished: “That duty to serve my constituents will remain my greatest motivation.”
The hour-long session, which her husband Philip watched from the public gallery, saw MPs from across the political divide pay tribute to May’s public service and sense of duty despite voicing their disagreement with many of her policies.
Jeremy Corbyn, who tapped his fingers on his knee amid the standing ovation, was no doubt reeling from May’s parting shot across the floor earlier in the exchanges.
“As a party leader who has accepted when her time was up, perhaps the time is now for him to do the same,” she gibed.
To add insult to injury, Labour MP Ian Austin later said the “vast majority” on his benches agreed.
Corbyn had earlier paid tribute to May’s “sense of public duty” before highlighting increases in poverty, violent crime, NHS waiting times and school class sizes in the past three years, among other things.
Television footage from a news helicopter over parliament showed parliamentary staff lined up in a courtyard, clapping and taking photos on their phones as she walked to her car to return to her Downing Street residence for the final time.
May took over as prime minister in the aftermath of the 2016 vote to leave the European Union and is standing down just over three years later having failed to deliver Brexit, her divorce deal with the bloc rejected three times by a deeply divided parliament.
One of her final acts as prime minister was to receive the resignations of Philip Hammond, David Gauke and Rory Stewart from their cabinet roles.
Her effective deputy prime minister David Lidington also announced he was standing down from the government.
May’s farewell speech in Downing Street was interrupted by a cry of “stop Brexit” from a protester outside.
In reply she joked: “I think not.”
– with AAP
Want to comment?
Send us an email, making it clear which story you’re commenting on and including your full name (required for publication) and phone number (only for verification purposes). Please put “Reader views” in the subject.
We’ll publish the best comments in a regular “Reader Views” post. Your comments can be brief, or we can accept up to 350 words, or thereabouts.
InDaily has changed the way we receive comments. Go here for an explanation.
Local News Matters
Media diversity is under threat in Australia – nowhere more so than in South Australia. The state needs more than one voice to guide it forward and you can help with a donation of any size to InDaily. Your contribution goes directly to helping our journalists uncover the facts. Please click below to contribute to InDaily.