In a statement on the steps of 10 Downing Street, Ms May said she would resign as Conservative leader on June 7.
The PM broke down as she said it had been "the honour of my life".
The dramatic announcement came after the chair of the Tories' backbench 1922 Committee, Sir Graham Brady, met her in Downing Street to demand a timetable for her departure.
Following the speech, International Trade Secretary Liam Fox tweeted: "Theresa-may has acted with dignity and honour in pursuit of what she believes to be in the national interest, the hallmark of her time in public life."
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