The domino-style spectacle Monday was just the latest twist to a British political season that has been marked by constant surprise and upheaval.
As May takes over, she will be under pressure to trigger the country's withdrawal from the 28-nation European Union.
The 59-year-old May will take office having never been voted into the job by anyone beyond lawmakers in the ruling Conservative Party. She will be the first female prime minister in Britain since Margaret Thatcher stepped down in 1990.
Cameron said he will chair his last cabinet meeting on Tuesday, and that on Wednesday he would attend Prime Minister's Questions.
"After that I expect to go to the palace and offer my resignation so we will have a new prime minister in that building behind me by Wednesday evening," he said.
Leadsom's sudden withdrawal appeared to have caught May's campaign team - and the rest of British politics - off guard.
Leadsom, a relative unknown, had advocated for a British exit from the European Union. She came under intense criticism over the weekend after suggesting to the Times of London that motherhood would make her a better fit for prime minister, and later told the Daily Telegraph that the pressure had been "shattering." But she did not mention the controversy in her remarks Monday.
May, the country's home affairs secretary, had campaigned for Britain to stay in the European Union. But the no-nonsense May had repeated that Britain cannot ignore the referendum outcome.
"I couldn't be clearer: Brexit means Brexit, and we're going to make a success of it," she said at a campaign rally Monday morning, before Leadsom quit the race.
The key question now is timing.
May had earlier suggested that the country would wait until next year to trigger its departure. But with European leaders and pro-Brexit politicians pushing for earlier action, she could find that her hand has been forced.
Britain voted last month in a national referendum to get out of the EU, leading Cameron to announce plans to resign after his pro-EU side suffered the loss.
The winner of the leadership contest was supposed to take over from Cameron shortly after results were to be announced on Sept. 9.
"In some ways, given the urgency of the economic and political situation the country is facing, it may have been the best thing to do for the sake of the country and the party," said Tim Bale, professor of politics at London's Queen Mary University.
Bale said that although the campaign was only days old, Leadsom had already shown that she shown would "have difficulty coping with the top job in British politics."
Although another candidate could have conceivably been named to the ballot, there appeared to be no appetite within the party for a summer-long contest involving a vote of the Conservative Party's 150,000 grass-roots members. May had been a strong favorite to win, having secured a majority of votes among Tory lawmakers last week.
In announcing her decision in front of a dark-brick townhouse in central London, Leadsom endorsed May to take the job and argued that her rival be allowed to take over as soon as possible. Leadsom said her departure from the race will allow the country to move forward with its Brexit plans.
"A nine-week leadership campaign at such a critical moment for our country is highly undesirable," she said, adding that "business needs certainty."
Michael Gove, the justice secretary who finished third in last week's winnowing of candidates, also endorsed May on Monday, and said she should be allowed to take office as soon as possible.
Boris Johnson, the former London mayor and a Leadsom backer, quickly switched allegiances and lined up behind May.
"It is vital that we respect the will of the people and get on with exploiting new opportunities for this country," Johnson said in a statement, referring to the EU vote.
The sudden shift in the leadership race coincides with a visit to New York by Britain's finance minister, George Osborne, in efforts to calm global investors uneasy over Britain's plans for an EU break.
The push to quickly bring in a new prime minister also came as the opposition Labour Party continued to be mired in infighting. Angela Eagle, a former top deputy of party leader Jeremy Corbyn, announced Monday that she would challenge Corbyn for his job.
The leftist Corbyn has already lost a confidence vote among Labour members of Parliament, but has refused persistent calls to step aside.
Dissidents within Labour, including Eagle, have argued that he was only an ambivalent campaigner for "remain" in the EU referendum and is ill-equipped to lead the party in a general election if the Conservatives decide to call one in order to renew their mandate.
The Conservatives, also known as Tories, won a majority in last year's election, which is why they did not necessarily need to call a fresh vote in order to appoint a new prime minister. But both Labour and the Liberal Democratic Party on Monday called for a new election before the next scheduled vote, in 2020.
"Tories now have no mandate," tweeted Tim Farron, leader of the centrist Liberal Democrats. "Britain deserves better than this."
May has said that she would not call a new election as prime minister. But she had also said before Monday that she thought it was important to give voters a choice, even if balloting was only open to Conservatives.
Before the referendum, May had been seen as a relative long-shot for prime minister, often rating mention for the job only behind Johnson and Osborne. But as better-known candidates were knocked out, May benefited from having kept a low-profile during the referendum campaign. That positioning has allowed her to campaign as a unity candidate capable of bringing back together the party's warring "leave" and "remain" factions.
