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.
It 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 Mr Mugabe under house arrest.
After the resignation announcement, lawmakers roared in jubilation.