May had a meeting with the Conservatives ruling 1922 Committee at Westminster on Thursday to decide her fate.
Pressure has been building from rebel MPs over the PMs handling of Brexit – with open calls for her to resign.
Sir Graham Brady, chairman of the 1922, revealed today May has agreed to set a timetable for her departure from Downing Street.
He confirmed the will be another meeting early in June to agree the details of her exit – and Tory MPs expect to have new leader by September.
It comes as May is set to bring back her Withdrawal Agreement to the House of Commons to finally reach a consensus on Brexit.
And it has occurred as the Tories face humiliation in next weeks EU Elections – with some polls putting them as low as fifth place.
“We will agree a timetable for the election of a new leader of the Conservative and Unionist Party”
Sir Graham Brady
Sir Graham said in a statement "The Prime Minister is determined to secure our departure from the European Union and is devoting her efforts to securing the second reading of the Withdrawal Agreement Bill in the week commencing June 3 2019 and the passage of that Bill and the consequent departure of the United Kingdom from the European Union by the summer.
"We have agreed that she and I will meet following the second reading of the Bill to agree a timetable for the election of a new leader of the Conservative and Unionist Party."
The statement means that, yet again May has resisted calls for her to name the date of her departure from No 10.
He added the discussions with the Prime Minister were "frank", and confirmed his meeting with her would take place regardless of whether the Withdrawal Agreement Bill passes second reading next month.
END OF MAY: Theresa May is expected to be out by September (Pic: AFP)
Sir Graham told reporters: "We have agreed to meet to decide the timetable for the election of a new leader of the Conservative Party as soon as the second reading has occurred and that will take place regardless of what the vote is on the second reading – whether it passes or whether it fails."
Sir Graham added: "It was a very frank discussion, I tried to make sure that all the views represented on the executive were expressed and we had a very frank exchange with the Prime Minister."
The announcement came as Boris Johnson confirmed he would be a contender when the contest took place.
According to the BBC, the former foreign secretary told a business event in Manchester: "I'm going to go for it. Of course I'm going to go for it."
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BABY BLUE WAVE: Nigel Farage's new Brexit Party is expected to win big in the EU Elections (Pic: EPA)
The meeting between Mrs May and the 1922 executive took place amid a growing clamour from Tory backbenchers for her to set a date for her exit from Downing Street.
Conservative MPs blamed frustration at her failure to take Britain out of the EU as planned on March 29 for the heavy losses the party suffered in the English council elections.
They fear the party is heading for another drubbing at the hands of Nigel Farage's new Brexit Party in the European elections on May 23.
Reacting to the news of Mays imminent departure, Farage said: “Gutless, useless and exactly what I expected. Really, really pathetic."
TALKS: Jeremy Corbyn and Theresa May have been attempting to solve Brexit (Pic: GETTY)
Farage has been exploiting the political paralysis with Westminster, with The Brexit Party polling as high as 34% according to YouGov.
Tories meanwhile are sitting at just 10%, while Labour have 16%, the LibDems on 15% and the Greens on 11%.
In a general election, the poll suggested the Tories would be neck and neck with Labour on just 24%, with the Brexit Party on 18% and Lib Dems on 16%.
May has been attempting to find a consensus with Labour over Brexit in a bid to force her deal through the Commons.
MAYDAY! MAYDAY!: Theresa May arrives in Westminster ahead of the meeting with the 1922 (Pic: REUTERS)
Conservatives are also still recovering from a bruising performance in the local elections, which saw them lose 1,330 councillors.
Tory Brexiteer Andrew Bridgen said he hoped there would be a leadership contest over the summer and a new prime minister in place by September.
He told the Press Association: "We will be able to have the Conservative Party leadership concluded well before the end of thRead More – Source[contf] [contfnew]