A Conservative leadership contest will take place this summer and a new prime minister will be in place in time for the party conference in October.
In the meantime, Mr Johnson will continue as prime minister.
He had vowed to “keep going” following a wave of resignations from the government over his leadership but has now decided to step down.
Senior members of his cabinet, including chancellor Nadhim Zahawi, urged him to resign and “leave with dignity”.
Mr Johnson is expected to give a resignation statement outside No 10 Downing Street later.
Mr Johnson became prime minister in July 2019 after winning a Tory leadership contest, and went on to win an historic landslide general election victory five months after that.
He won the election vowing to “get Brexit done” but his government has been dogged by a series of controversies in recent months, not least a police investigation into parties in Downing Street during lockdown.
The revolt this week was triggered by revelations about the prime minister’s handling of sexual misconduct allegations against former Deputy Chief Whip Chris Pincher.
BBC political editor Chris Mason said Graham Brady, the chairman of the 1922 Committee of backbench Tory MPs, has met the prime minister to tell him he has lost the confidence of the party.