A No 10 source said Mr Johnson spoke to Sir Graham Brady, chairman of the Conservative 1922 Committee, to inform him of his decision.
“The Prime Minister has spoken to Graham Brady and agreed to stand down in time for a new leader to be in place by the conference in October,” a No 10 source said.
Prime Minister: this is not sustainable and it will only get worse: for you, for the Conservative Party and most importantly of all the country. You must do the right thing and go now. pic.twitter.com/F2iKT1PhvC
— Nadhim Zahawi (@nadhimzahawi) July 7, 2022
Mr Johnson will make a statement later today confirming the decision.
The resignation comes after the Prime Minister haemorrhaged support among his ministers and MPs.
More than 50 MPs have resigned from government or party roles since Tuesday night, when the mass exodus was triggered by the resignations of Rishi Sunak and Sajid Javid from the Cabinet.
The Prime Minister had sought to defy his critics and carry on in office, despite warnings from Cabinet colleagues that this was not sustainable.
But resignations continued and Chancellor Nadhim Zahawi – who was only appointed to the role on Tuesday – went public with his call for the Prime Minister to quit.
The timetable for the Tory leadership contest will be agreed between the 1922 Committee, which runs the parliamentary proceedings to whittle the candidates down to two, and Conservative headquarters.
But critics of the Prime Minister suggested he should not be allowed to remain in office until the autumn.
George Freeman, who quit as science minister on Thursday morning, said that now Mr Johnson had “finally done the decent thing” he should “hand in the seals of office, apologise to Her Majesty, allow her to appoint a caretaker under whom ministers can serve, so the Conservative Party can choose a new leader properly”.