About 150,000 members of the Conservatives Party across Britain will now vote by postal ballot to decide whether May or Leadsom become Britain's first woman prime minister since Margaret Thatcher was forced from office in 1990.
Anti-EU campaigner and ex-London mayor Boris Johnson, who is backing Mrs Leadsom, 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'.
Prime Minister David Cameron announced that he would resign by October after the Brexit vote, saying, "I was absolutely clear about my belief that Britain is stronger, safer and better off inside the European Union..." During the referendum campaign she took a low-key stance in favor of Britain remaining in the European Union, while Leadsom was a prominent voice in the winning Leave camp.
"What we have seen is a gradual encroachment with some really quite brutal activities that we need to try to get under control".
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".
And regardless of who they pick, the new leader of Britain will become the second woman ever to hold the keys to Downing Street.
It means the Conservative Party is set to give the country its second female prime minister.
Five Conservative contenders had initially been campaigning for Cameron's post, but that number is now down to two, with results expected to be announced on September 9. She polled 84 votes to secure her place in the party-wide fight.
May had an upper hand in the first stage of selections, which was done via voting by 330 party members of House of Commons.
Leadsom, who entered Parliament in 2010 after a career in financial services, has less political experience than May, and has faced allegations from rivals that she exaggerated the seniority of her financial sector jobs.
"She might command the support of party members; but she would already have been rejected by MPs, twice as many of whom would have voted for her opponent".
"Andrea Leadsom is undoubtedly the outsider, but she will play up her Brexit credentials", said Al Jazeera's Barnaby Phillips on Thursday in Westminster. Leadsom supported the "leave" campaign.