A letter from Mr Mugabe said the decision was voluntary and he had made it to allow a smooth transfer of power.
The surprise announcement halted an impeachment hearing that had begun against him and sparked wild celebrations on the nation's streets.
The ruling Zanu-PF party says former vice-president Emmerson Mnangagwa will succeed Mr Mugabe, in power since 1980.
Mr Mnangagwa's sacking earlier this month triggered a political crisis.
