Theresa May has appointed Amber Rudd to replace her at the UK Home Office and ally Philip Hammond becomes the chancellor of the exchequer.
George Osborne, whose career was inextricably linked with Mr Cameron’s fortunes, has left government amid claims he was sacked.
David Davis will become Secretary of State for Brexit and Michael Fallon is to stay on as defence secretary.
The flurry of appointments came within hours of Ms May taking office.
In a speech in Downing Street, Britain’s second female prime minister said that the decisions of her administration would be driven not by the interests of “the privileged few” but those of voters struggling with the pressures of modern life.
“I know you are working around the clock, I know you are doing your best and I know that sometimes life can be a struggle,” she told voters.
“The government I lead will be driven not by the interests of the privileged few but by yours. We will do everything we can to give you more control over your lives.”
At the age of 59, Ms May becomes the 13th holder of the office of British prime minister of Queen Elizabeth II’s reign.
She was invited to form a government by the Queen in a simple ceremony at Buckingham Palace less than half an hour after Mr Cameron had tendered his formal resignation to the head of state.
Her appointment came as she gave the Queen her hand and bent her knee in a traditional procedure known as “kissing hands”.
Earlier, the PM-designate sat alongside Mr Cameron as he answered questions to the prime minister for the last time in the House of Commons.
The outgoing PM was given a standing ovation by Conservative MPs as he said his farewell with the comment “I was the future once” — a self-deprecating reminder of the jibe he directed at Tony Blair as the fresh-faced new Tory leader in 2005.
Mr Cameron was accompanied by wife Samantha and children Nancy, Elwen, and Florence as he left 10 Downing Street for the last time as prime minister.
Just over an hour after her speech, foreign secretary Philip Hammond and then Boris Johnson entered Number 10, the former London mayor ignoring reporters’ questions.
Ms Rudd was next to enter Downing Street followed by Mr Fallon.
Mr Johnson again ignored reporters’ questions when he left Downing Street. Instead he just waved as he climbed into a ministerial car and was driven away.
David Davis, a former Tory leadership rival to Mr Cameron, was next to enter Number 10. He had backed Mr Johnson in the latest leadership race until he pulled out, when Mr Davis threw his support behind Mrs May.
Downing Street said later that Mr Fallon would be staying on as defence secretary.
As that was being announced, former defence secretary Liam Fox arrived at Downing Street where he was made international trade secretary.
He held the defence post from 2010 but resigned the following year over allegations he had given a close friend access to the ministry of defence and allowed him to join official trips overseas.