Cameron will cede power to 59-year-old May after visiting Buckingham Palace to resign tomorrow.
Until Monday, Cameron, 49, had been expected to remain in office for another two months.
But when Energy Minister Andrea Leadsom unexpectedly pulled out of the race yesterday, leaving only May, the home secretary, still in the running, Cameron announced that he would swiftly make way for the incoming leader.
Cameron had resigned in the wake of Britain's shocking vote to leave the European Union on June 23.
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The meeting was described as "emotional" by Culture Secretary John Whittingdale who said "there was a touch of sadness" to the Prime Minister and his ministers.
Cameron had announced he would be stepping down for a new prime minister to take the Brexit negotiations forward with the European Union a day after the June 23 vote in favour of Britain leaving the economic bloc.
"It was emotional but quite rightly we spent a lot of time on the Government business. But then we had a period in which people paid tribute to the extraordinary service the Prime Minister has given, led off by George Osborne and Theresa May our new prime minister. And then we looked forward to getting back to work," the leading Brexit campaigner told Sky News.
May, a known Euroskeptic, reiterated her commitment to Brexit yesterday.
"Brexit means Brexit, and we're going to make a success of it," she said.
"There will be no attempts to remain inside the EU. No attempts to rejoin it by the back door."
The pound has rallied against the dollar in the wake of the news that May would become prime minister, bringing a measure of political stability sooner than expected.
May will become the UK's second female Prime Minister after Thatcher from 1979 to 1990.