In it, Mr Mugabe – who had so far resisted pressure from the public, the army and his own party to step aside – said he was resigning to allow a smooth and peaceful transfer of power, and that his decision was voluntary.
The announcement abruptly halted an impeachment hearing that had begun against him on Tuesday.
‘I’m so happy’
Lawmakers from the ruling party and opposition roared with glee, and spontaneous scenes of joy erupted in the streets with people dancing, singing, honking car horns and waving flags.
“I’m so happy, wonderful, feeling so much excited, this is the greatest moment for our country,” Julian Mtukudzi told the AFP news agency.
“We have been having sleepless nights hoping and waiting and we are so happy. It’s over and it’s done.”
Media captionActivist and political candidate Vimbaishe Musvaburi breaks down in tears of joy
Activist and political candidate Vimbaishe Musvaburi broke down in tears of joy speaking to the BBC.
“We are tired of this man, we are so glad he’s gone. We don’t want him anymore and yes, today, it’s victory,” she said.
Zimbabwe’s next president
The ruling Zanu-PF party says former Vice-President Emmerson Mnangagwa will succeed Mr Mugabe.
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.