David Cameron will chair Cabinet for the final time today before Theresa May takes over as prime minister tomorrow.
The home secretary said she was “honoured and humbled” by yesterday's events which saw her skip the nine-week leadership race and secure the top job.
The sensational withdrawal of rival Andrea Leadsom from the Conservative leadership race fast-tracked the process and took the nation by surprise – including the prime minister.
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“None of us had any idea things would move so fast today, least of all the prime minister,” a No 10 spokesperson told The Sun.
Cameron has announced that he will tender his resignation after Prime Minister’s Questions on Wednesday.
He paid tribute to the home secretary, declaring in a statement outside No 10 yesterday: “She is strong, she is competent, she’s more than able to provide the leadership that our country is going to need in the years ahead and she will have my full support."
Chancellor George Osborne also welcomed May to her new post.
“I’ve sat around the Cabinet table with her for six years and she’s got the integrity, the strength and the leadership that our country needs,” he said.
May said she wanted to "build a better Britain" as she addressed the public for the first time as Conservative leader.
The prime minister-designate said outside the Houses of Parliament: “During this campaign my case has been based on three things.
"First, the need for strong, proven leadership to steer us through what will be difficult and uncertain economic and political times, the need, of course, to negotiate the best deal for Britain in leaving the EU and to forge a new role for ourselves in the world.
"Brexit means Brexit and we're going to make a success of it.
"Second we need to unite our country. And third, we need a strong, new positive vision for the future of our country - a vision of a country that works not for the privileged few but works for every one of us.
"Because we're going to give people more control over their lives and that's how together we will build a better Britain."
Jeroen Dijsselbloem, the Dutch finance minister who chairs eurozone meetings, hailed the victory of May – and suggested it could lead to early negotiations on Britain's withdrawal from the European Union.
“We will have to find solutions for Brexit which has been causing a lot of problems particularly for the UK but also for Europe,” he said.
“The sooner we can sort out this problematic situation the better.”
May has so far rejected calls from Labour, the Liberal Democrats and others for a snap general election to confirm her mandate with the public.