A letter from Robert Mugabe, 93, read out by the speaker of parliament said the decision was voluntary and he had made it to allow a smooth transfer of power.
The news abruptly halted an impeachment hearing that had begun against him.
The ruling Zanu-PF party says former VP Emmerson Mnangagwa will succeed Robert Mugabe, in power since 1980.
Emmerson Mnangagwa’s dismissal earlier this month triggered a political crisis.
The move had been seen by many as an attempt to clear the way for Grace Mugabe to succeed her husband as leader and riled the military leadership, who stepped in and put Robert Mugabe under house arrest.
After the resignation announcement, lawmakers roared in jubilation.
Robert Mugabe was until his resignation the world’s oldest leader. He had previously refused to quit despite last week’s military takeover and days of protests.
According to the constitution, Robert Mugabe’s successor should be the current vice-president, Phelekezela Mphoko, a supporter of Grace Mugabe.
However, Zanu-PF chief whip Lovemore Matuke told Reuters that Emmerson Mnangagwa would be in office “within 48 hours”.
Speaking from an undisclosed location earlier on November 21, Emmerson Mnangagwa said he had fled abroad two weeks ago when he learned of a plot to kill him.
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