He confirmed the resignation in a letter sent to the speaker of that country’s parliament.
Mr Mugabe had previously refused to resign despite last week’s military takeover, and days of protests against his rule.
He has been in power since independence in 1980.
In a live TV address last Sunday, Mr Mugabe said he would preside over his party the Zanu PF’s congress in December, despite pressures on him to resign.
The Zanu-PF had earlier sacked him as party leader, and gave him less than 24 hours to resign as president or be impeached.
He was expected to resign hours later but he stated in the TV broadcast that he will continue to stay in power.