The ruling Conservative party's members will choose from two candidates backed by most MPs and the victor is due to be named on September 9.
In the dramatic vote last night, Mrs May won the support of 199 of her Parliamentary colleagues - 115 more than Mrs Leadsom, who was little known until her meteoric rise only a few weeks ago.
Following the bruising European Union referendum campaign and the resignation of David Cameron, the Home Secretary has insisted she can unite the party.
'I am particularly anxious about Andrea Leadsom's views, ' Cooper said at the Stonewall Education For All conference.
The victor will be announced on September 9, handing the keys of 10 Downing Street to a woman occupant since 1979 when Margaret Thatcher became the country's first ever female prime minister.
We don't yet know who the next Prime Minister of Britain will be, but we now know it will be a woman.
The results were announced at Westminster by Conservative MP Graham Brady, the chairman of the backbench 1922 Committee. Now that the vote has set the United Kingdom on a course for separation from the E.U., May is pushing an even harder line, refusing to guarantee that E.U. citizens living in Britain will be allowed to stay in the country.
The duo will take part in a series of hustings around the country over the summer.
Now the Tories' 150,000-strong membership will vote on who will become the next leader of the Conservative's - and Britain's second female Prime Minister: Mrs May, a Remain campaigner, or Mrs Leadsom, a member of the Brexit campaign.
During the week of campaigning, Leadsom spoke out against same-sex marriage.
And a former senior advisor to Cameron, Andrew Cooper, added: "Theresa May told Tories in 2002 they were 'nasty party.' David Cameron spent 11 yrs trying to fix it. Andrea Leadsom = nasty party again".
Firstly, for his last-minute decision to withdraw support for Boris Johnson and enter the race himself, and secondly for the text his campaign manager sent to May supporters urging them to vote tactically to keep Leadsom off the ballot.
Mrs May also said there should be no general election before 2020 and no "emergency" Brexit budget - and that she would abandon the target of eliminating Britain's Budget deficit by the end of the decade - a day before the chancellor himself abandoned it.
Leadsom has been an MP since 2010 and serves as the energy and climate change minister.
Andrea Leadsom reportedly made the comments to today's Times newspaper after Theresa May spoke, in an interview earlier this week, of how she and her husband were unable to have children.