In a speech earlier, Mrs Leadsom pitched herself as the "prosperity not austerity" candidate in the race to become the next Prime Minister.
Ms May won 165 votes in a first ballot of Conservative members of parliament and Andrea Leadsom, a junior energy minister, won 66, increasing the likelihood that Britain will get only its second woman Prime Minister after Margaret Thatcher.
Gove, 48, came third in Tuesday's first-round vote and is seen by some Tories as untrustworthy after he ditched his support for former London Mayor Boris Johnson - who had been expected to run for Conservative leader - and declared himself a candidate instead.
A ballot with Leadsom and May's names will be mailed to the 150,000 some Conservative Party members and results will be announced September 9.
Both now go forward to a ballot of Conservative party members to decide which of them will become the UK's second female Prime Minister.
Ms May, who opposed Brexit in last month's referendum, and Ms Leadsom, who campaigned to leave the European Union, will now compete for the votes of about 150,000 Conservative party members.
May, 59, came out of the vote with 199 votes from the party's 330 members of Parliament. The victor will replace Prime Minister David Cameron who announced his resignation after Britons voted on June 23 to leave the European Union.
The two candidates were on opposing sides ahead of the European Union referendum, with Mrs May - like Ms Davidson - backing Remain, while Mrs Leadsom was a prominent figure in the victorious Leave campaign.
The announcement was made on July 7 as Conservative MPs started to cast their votes on who should next lead the party.
"Andrea Leadsom is undoubtedly the outsider, but she will play up her Brexit credentials", said Al Jazeera's Barnaby Phillips on Thursday in Westminster. "In all the hustings debates, Andrea more than held her own".
"We need to get on with it", she said.
"She is now well placed to win and replace the absurd gloom in some quarters with a positive, confident and optimistic approach, not just to Europe, but to government all round", he said. "Isn't this the new sort of Tory party?" Leadsom received the vote of 84 MP's.
The Justice Secretary posted a tweet wishing May and Leadsom luck shortly after the announcement.
Mrs Leadsom was a high-profile Vote Leave voice and has said Article 50 should be triggered "as soon as possible" and has secured the support of controversial UKIP donor Arron Banks.