Home Secretary Mrs May won 199 votes in the second-round ballot of MPs at Westminster today, while Justice Secretary Mr Gove took just 46 votes.
Energy minister Mrs Leadsom, whose leadership ambitions were boosted after playing a major role in the Brexit campaign, won the backing of 84 of her fellow MPs.
But the final decision on which of them will become the UK’s second female prime minister after Margaret Thatcher will be made by Conservative Party members in a postal ballot due to end on 9 September.
Mrs May said: “This vote shows that the Conservative Party can come together - and under my leadership it will.
“I have said all along that this election needs to be a proper contest. And now it is time for me - and my team - to put my case to the Conservative Party membership.
“That case comes down to three things. Because we need strong, proven leadership to negotiate the best deal for Britain as we leave the European Union, to unite our party and our country, and to make Britain a country that works not for a privileged few but for every one of us.
“Those are the things my colleagues have voted for in overwhelming numbers today, and I am confident they will win the support of our members - and the support of the country as a whole.”
Mr Gove, who won the backing of two fewer MPs than in the first round of voting, said he was “naturally disappointed” that his leadership bid had failed but welcomed the fact that the next prime minister would be a woman.
The Scot said: “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 and I know whichever one of the two wins they will lead this country well.”
While Mrs May enjoys a clear advantage among Tories at Westminster, she will be acutely aware that Mrs Leadsom could attract votes from Eurosceptic activists who want a “Brexit prime minister” to oversee withdrawal negotiations.
Although signed up to the Remain camp, Mrs May maintained a low profile during the referendum, and sought to neutralise the issue as she launched her leadership bid by making clear she would not seek to overturn the result and declaring: “Brexit is Brexit.”
In a speech outside Parliament after the ballot, Mrs May insisted she had won support from MPs from across the party “left and right, leavers and remainers”.
The new prime minister will be chosen by an electorate of around 150,000 Conservative Party members.
Mrs Leadsom’s campaign chief Tim Loughton said the run-off represented a “quirky” choice for the Tories.
“They both went to state schools, they are both women, hey, that’s pretty quirky for the Tory party. Isn’t this the new sort of Tory party?”
Scottish Conservative leader Ruth Davidson revealed she is backing Mrs May to be the UK’s next prime minister.
She described Mrs May as a “proper grown up”, adding that she is “best placed to navigate the stormy waters ahead”.
The Scottish Conservative leader announced her preferred candidate in the ballot to replace David Cameron after the contest was reduced to two MPs. Scottish Secretary David Mundell has also backed Mrs May as leader.
Ms Davidson said: “Serious times call for serious people and Theresa is a proper grown up who will assess all the evidence before making a decision.
“I trust her in the tough negotiations ahead to be able to go eyeball to eyeball with (German Chancellor) Angela Merkel, and not blink.”
She added: “It is important that the new prime minister is alive to the threats to our union that the SNP will try to engineer. And it is no surprise that those in leadership positions in the Conservative Party in Scotland - myself in Holyrood, Annabel Goldie in the House of Lords, David Mundell in the Commons and our MEP Ian Duncan - are all agreed that the person most able to protect Scotland’s place in the United Kingdom is Theresa May.
“As the leader of the party in Scotland, I have a responsibility to take the selection of our next UK leader - and prime minister - seriously indeed. I do. And that’s why I can say without hesitation that I believe Theresa May is best placed to navigate the stormy waters ahead.”
Former Tory leader Iain Duncan Smith, who is backing Mrs Leadsom, said she had “real steel” but within the “velvet glove of compassion”.
He said: “I think Andrea Leadsom is fantastically qualified for the job.”
“It says to women all over the country ‘you can get to the top’.”
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.
On Tuesday Mr Gove won the support of 48 MPs but on Wednesday his campaign manager Nick Boles was forced to apologise after it emerged he had been encouraging tactical voting because he was “seriously frightened” about Mrs Leadsom getting on to the ballot.
Meanwhile, Mrs Leadsom - who has faced questions about Ukip support for her leadership bid - was given the backing of the party’s outgoing leader Nigel Farage.
He tweeted: “Congratulations to @andrealeadsom. Important the next Prime Minister is a Brexiteer - she has my backing.”
When she launched her campaign Mrs Leadsom insisted she had “no allegiance” to Ukip as she said the Brexit negotiating team would come from within the Government.
Boris Johnson, whose own hopes of the leadership were effectively torpedoed by Mr Gove’s late entry into the race, is backing Mrs Leadsom.
The former London mayor 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.”