Ms May won 199 votes and Ms Leadsom 84 in a second ballot of lawmakers of the governing Conservative Party.
Britain is on track to have its second female leader after the ruling Conservative Party narrowed down its choice of someone to succeed outgoing Prime Minister David Cameron to two women.
In the first round, Mrs May won 165 votes, Mrs Leadsom 66, Mr Gove 48, Stephen Crabb - who later withdrew - 34 and Liam Fox - who was eliminated - 16.
But the final decision will now be made by Conservative Party members in a postal ballot due to end on September 9.
David Cameron, the Conservative prime minister, campaigned to stay in the EU.
The victor will become the country's second female prime minister following Margaret Thatcher, who held office from 1979 to 1990.
'This vote shows that the Conservative Party can come together - and under my leadership it will.
The next British prime minister will be a woman.
She also promised to provide, "strong leadership to negotiate the best deal for Britain as we leave the European Union, to unite our Party and our country".
Leadsom, 53 years old, has been in Parliament since 2010 and is considered less experienced than May.
Leadsom lacks cabinet experience but played an impressive role in campaigning for a Brexit prior to the public voting for it on June 23.
"Following last week's referendum, our country needs strong leadership to steer us through this period of economic and political uncertainty", May said in launching her bid last week.
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".