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.
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“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.
Mr Johnson will make a statement to the country 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.
It means Boris Johnson is the third Conservative prime minister to be brought down by Tory infighting in the space of six years.