Mrs May had been expecting a nine-week Conservative leadership race, but rival Andrea Leadsom withdrew on Monday.

Mr Cameron will tender his resignation to the Queen on Wednesday, leaving Mrs May, home secretary since 2010, to appoint her own ministerial team.

Mrs May said she was "honoured and humbled" to be taking over and pledged to make a success of the UK's EU exit.Mrs Leadsom's surprise announcement left Mrs May, who had been the front runner, as the only remaining candidate to take over the leadership of the Conservative Party and, therefore, also become prime minister.

Flanked by dozens of Conservative MPs, Mrs May praised Mr Cameron for his stewardship of the party and the country and paid tribute to Mrs Leadsom for her "dignity" in withdrawing her leadership bid.

But senior Labour MP Jon Trickett has joined the Lib Dems and Green Party in calling for a snap general election.

Mr Trickett, Labour's general election co-ordinator and an ally of leader Jeremy Corbyn, said it was "crucial" to have a "democratically elected prime minister" and said he was putting the party on "general election footing".

Mrs May has rejected such demands.

BBC political editor Laura Kuenssberg said EU negotiation, controlling immigration and managing the economy were "huge issues" that would challenge Mrs May's desire for a "steady as she goes" approach.Theresa May was expecting a nine-week leadership contest, giving her plenty of time to think about her new team.

Instead, she got just 48 hours notice before having to walk into Downing Street and assemble a government.

As someone who wanted the UK to stay in the EU, there will be pressure to give prominent cabinet roles to those who backed Brexit.

Mrs May has promised radical social and economic reform - fuelling speculation over the future of current senior figures.

With limited time to make delicate political choices, the new prime minister must weigh change versus continuity, while trying to unite the Conservative Party after a bruising EU referendum campaign.

So far, Tory MPs have rallied round their new leader, but rival political parties have questioned her mandate after the leadership contest was cut short.

Sources close to Mrs May said she'd been very clear - there would be no general election.

Former chancellor Ken Clarke - who supported Mrs May in the final ballot - said the new leader and prime minister needed to "balance the party" in her cabinet appointments.

"She's got a real problem of bringing the warring wings of the party together. She'll combine her own strong personal opinions about who she wants to work with, with a desire to bring the party together," he said.

But he cautioned that the party's small parliamentary majority would not make the task "easy".

"To actually get the real head-bangers together on both sides and to see four years of government through will require some political skill… but she's pragmatic, she'll want to get on and do things," he said.

Northern Ireland secretary Theresa Villiers - who backed Mrs Leadsom in the contest - said she was sure Mrs May would "want to draw on talents from across the parliamentary party".

Asked whether Mrs May should balance the cabinet, she said: "I certainly hope that both Remain and Leave campaigners will be represented in the cabinet."

But she urged all colleagues, whatever the outcome of the reshuffle, to be "incredibly supportive" of the new prime minister, saying a "stable government" was needed.Mrs May has said her leadership bid had been based on the need for "strong, proven leadership", the ability to unite both party and country and a "positive vision" for Britain's future.

And in a message perhaps designed to reassure Brexit-supporting colleagues on Monday, Mrs May, a Remain campaigner, said: "Brexit means Brexit - and we're going to make a success of it."

Mr Cameron, who has been prime minister since 2010, decided to quit after the UK's referendum vote to leave the EU, having campaigned for the losing side.

He praised Mrs May as "strong" and "competent" and said she was "more than able to provide the leadership" the UK needs in the coming years.

"She will have my full support," he added.

Announcing her decision to pull out of the contest on Monday, Mrs Leadsom, who was a leading light of the Brexit campaign, said a nine-week leadership campaign at such a "critical time" for the UK would be "highly undesirable", and she gave her backing to Mrs May.

Mrs Leadsom had apologised to Mrs May on Monday after suggesting in a weekend newspaper interview that being a mother made her a better candidate for the job than the home secretary.