Mr Johnson had sought to defy his critics and remain in office, despite warning from Cabinet colleagues that this was not sustainable.
But the resignations continued and made clear his position as Prime Minister was untenable.
PM to make public statement
Mr Johnson will make a public statement to the country later today confirming his decision to resign.
He 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.
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 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.”
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 argue Mr Johnson 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”.
Britain needs a ‘fresh start’
Sir Keir Starmer welcomed the news of Mr Johnson’s resignation as leader of the Conservative Party, saying it is “good news for the country”.
But the Labour leader argued the resignation should have “happened long ago” and called for a “proper change of government”.
He said: “It is good news for the country that Boris Johnson has resigned as Prime Minister. But it should have happened long ago.
“He was always unfit for office. He has been responsible for lies, scandal and fraud on an industrial scale. And all those who have been complicit should be utterly ashamed.
“The Tory party have inflicted chaos upon the country during the worst cost-of-living crisis in decades. And they cannot now pretend they are the ones to sort it out.
“They have been in power for 12 years. The damage they have done is profound.
“Twelve years of economic stagnation. Twelve years of declining public services. Twelve years of empty promises.
“Enough is enough. We don’t need to change the Tory at the top – we need a proper change of government.
“We need a fresh start for Britain.”