Britain is on track to have its first woman prime minister since
The winner of the contest will replace Prime Minister
In a ballot of
For the runoff, about 150,000 Conservative Party members across the country can vote for May or Leadsom by postal ballot. The results are expected to be announced Sept. 9.
May, 59, has been Britain's home secretary since 2010 and a member of Parliament since 1997.
She has a long track record in government but campaigned with Cameron for Britain to remain a member of the EU, a factor that some observers say should prevent her from leading the country as it seeks to negotiate the terms of the so-called
"I'm delighted to have won so much support from my colleagues," May said outside the Houses of Parliament after the results were announced. "This vote shows that the Conservative Party can come together and that under my leadership it will."
Leadsom, 53, campaigned for the Leave side. Although not as high profile as May, she put in strong performances during two TV debates during the referendum campaign.
She has also emphasized that her background in finance make her well placed to hold the keys to "Number 10," or 10 Downing Street in London, the government's headquarters and prime minister's residence.
"I think what people want in this country is somebody that says what they mean, means what they say, acts with integrity," Leadsom said.
Five members of Parliament from the Conservative Party had originally put their names forward to succeed Cameron, but they were whittled down to two during rounds of voting.
A total of 330 Conservative members of Parliament were eligible to vote. Only Cameron abstained.
Gove said he was "naturally disappointed" he would not be prime minister but said both women fully deserved to be in the final two.
"Whoever the next prime minister of this country will be, it will be a female prime minister and a female prime minister who has formidable skills," he said.
As soon as Cameron announced he was stepping aside as prime minister, all eyes turned to Boris Johnson, the most high-visible Leave campaigner who many believe made a tactical decision to join the pro-Brexit camp because of his political ambitions for the top job.
But the former London mayor surprised the country by announcing he would not seek to be prime minister after Gove, his main ally on the referendum trail, announced Johnson was not up to the job and threw his own name into the ring instead.
The move has been likened to an episode of the political TV series "House of Cards" and may have ultimately done irreparable damage to Gove's reputation.
Whichever candidate wins the runoff will not only become the country's second woman prime minister – Thatcher governed from 1979 to 1990 -- but will immediately face a tough job.
The new prime minister will be expected to unite the party and country, which have become deeply divided during the referendum campaign, and strive to negotiate the terms of Britain's exit from the 28-member European Union.
May or Leadsom will have to grapple with the complex issues around immigration and free trade while trying to ensure that that economy does not falter.
The future prime minister also can expect to be closely watched from the sidelines by ardent Leave campaigners like Nigel Farage, who announced he was stepping down as leader of the UK Independence Party this week after reaching the pinnacle of his political objectives by securing a Leave vote.
"Congratulations to @andrealeadsom. Important the next Prime Minister is a Brexiteer - she has my backing," he wrote on Twitter.
Boyle is a special correspondent.
2:21 p.m.: This article has been updated with Times reporting.