There had originally been five contenders to succeed Cameron, who had announced his resignation after Britain voted to leave the European Union (EU) in June 23 referendum.
The contest now shifts to the Conservative Party rank and file, the 150,000 card-carrying party members whose votes will determine their next leader and thus prime minister. May is now leading the race, followed by energy minster Andrea Leadsom who received the backing of former London mayor Boris Johnson yesterday.
"Not many countries have had one woman leader, never mind its second - it's ironic that Labour have made a lot of noise about its all-woman shortlists but we've got one entirely on merit".
But Ms Davidson said: "I think it has got to be someone who can unite both the country and the party, and I think Theresa May is the only one who can do that".
In a speech delivered after the results were announced, Mrs May said: "I'm delighted to have won the support from my colleagues".
The Home Secretary has promised "strong, proven leadership" to negotiate Brexit, while the rank outsider Mrs Leadsom has promised "prosperity, not austerity". The victor will become the second woman prime minister in Britain after Margaret Thatcher.
May and Leadsom will now begin their campaigns to convince the wider Conservative party membership around the country for a final round of voting with the victor set to be declared on September 9.
Mrs Leadsom came second behind Theresa May in the second round of voting among Tory MPs.
May hailed the result, saying it showed the Conservative Party could unite under her leadership after the divisive European Union referendum vote.
Chris Grayling, the chairman of Mrs May's campaign, told The Daily Telegraph that Mrs May would use the large number of MPs who backed her to win round members. May is now in the lead with 199 votes, and Leadsom is at 84.
Leadsom said she was "very grateful" to her team and "feeling very positive" about the future.
Mr Gove's support fell by two from his first-round performance, despite an effort to persuade supporters of Mrs May to lend him their votes in order to block Mrs Leadsom's progress.
"But I believe Andrea now, going to the country, has all that fantastic combination of steel, real grit, real determination, real world experience - working 25 years out of this place (Parliament), setting up charities - and in government she has that experience".
That could play well with grassroots party members, who have strong eurosceptic leanings.