Senior members of his cabinet, including Chancellor Nadhim Zahawi, urged him to resign and “leave with dignity”.
A No 10 source said Mr Johnson spoke to Sir Graham Brady, chairman of the Conservative 1922 Committee, this morning to inform him of his decision to stand down.
The source said: “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.”
Will Boris Johnson make a statement?
Mr Johnson will make a statement outside No 10 Downing Street later today confirming his decision to resign.
It is understood that his team is now writing his resignation letter and he will read it out at 12.30pm.
A No 10 spokesman confirmed: “The Prime Minister will make a statement to the country today.”
His decision to stand down came after he had been facing intense pressure to quit after more than 50 MPs resigned from all levels of government and called for him to go.
The mass rebellion began on Tuesday (5 July) after No 10 admitted Mr Johnson was told about allegations of inappropriate behaviour against disgraced former deputy chief whip Chris Pincher in 2019, but still appointed him in February.
Before the admission, ministers had been told to defend Mr Johnson on the airwaves and say he was unaware of "specific" allegations.
Mr Johnson later apologised and admitted appointing Mr Pincher was a "mistake", but the admission was quickly followed by the resignations of Health Secretary Sajid Javid and Chancellor Rishi Sunak.
What will happen next?
Mr Johnson will remain as Prime Minister until a successor is in place, which is expected to be by the time of the Conservative Party conference in October.
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.
However, 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”.
Lord Barwell, who served as Theresa May’s chief of staff, said the leadership election must be “relatively quick” and there was a “question whether the PM will be able to lead a caretaker government in the meantime, will enough ministers agree to serve?”
Business Secretary Kwasi Kwarteng also suggested he does not want Mr Johnson to stay in office until the autumn, saying a new leader is needed “as soon as practicable”.