In an emotional statement, she said she had done her best to deliver Brexit and it was a matter of “deep regret” that she had been unable to do so.
Mrs May said she would continue to serve as PM while a Conservative leadership contest takes place.
The party said it hoped a new leader could be in place by the end of July.
It means Mrs May will still be prime minister when US President Donald Trump makes his state visit to the UK at the start of June.
Mrs May announced she would step down as Tory leader on 7 June and had agreed with the chairman of Tory backbenchers that a leadership contest should begin the following week.On Friday, Foreign Secretary Jeremy Hunt became the latest MP to say that he would run for the party leadership, joining Boris Johnson, Esther McVey and Rory Stewart, who had already confirmed their intentions. More than a dozen others are believed to be seriously considering entering the contest.
In her statement, Mrs May said she had done “everything I can” to convince MPs to support the withdrawal deal she had negotiated with the European Union but it was now in the “best interests of the country for a new prime minister to lead that effort”.
She added that, in order to deliver Brexit, her successor would have to build agreement in Parliament.
“Such a consensus can only be reached if those on all sides of the debate are willing to compromise,” she said.