The country’s Parliament erupted with cheers as the announcement came in.
Mugabe will be succeeded by Zimbabwe’s recently fired vice president Emmerson Mnangagwa, who will take over within 48 hours.
Mugabe was expected to leave the post on Sunday during a televised speech but he refused to go, instead vowing to reform his government.
The parliamentary speaker stopped impeachment proceedings to say they had received a letter from Mr Mugabe confirming the resignation “with immediate effect”.
It read: ‘My decision to resign is voluntary on my part and arises from my concern for the welfare of the people of Zimbabwe and my desire for a smooth, non-violent transfer of power.’
The resignation comes at the end of a tumultuous week that began with the military moving in, angered by Mr Mugabe’s firing of his longtime deputy and the positioning of the widely unpopular first lady Grace Mugabe to succeed him.
Impeachment allegations against Mr Mugabe included that he “allowed his wife to usurp constitutional power” and that he is “of advanced age” and too incapacitated to rule.
Mr Mugabe, who has been in power since the end of white minority rule in 1980, was also accused of allowing unpopular first lady Grace Mugabe to threaten to kill the recently fired Vice President Emmerson Mnangagwa and other officials.
Mr Mnangagwa earlier said Mugabe should acknowledge the nation’s “insatiable desire” for a leadership change and resign immediately.
He said: “The people of Zimbabwe have spoken with one voice and it is my appeal to President Mugabe that he should take heed of this clarion call and resign forthwith so that the country can move forward and preserve his legacy.”
People soon thronged the streets of Harare, dancing and singing, to celebrate the news.
Cars began honking horns and people cheered in the streets, as the announcement made its way through the capital.
Mugabe presided over a period of economic and social crisis in Zimbabwe, where people are now on average 15% poorer than they were in 1980.
Prime Minister Theresa May said: ‘The resignation of Robert Mugabe provides Zimbabwe with an opportunity to forge a new path free of the oppression that characterised his rule.
‘In recent days we have seen the desire of the Zimbabwean people for free and fair elections and the opportunity to rebuild the country’s economy under a legitimate government.’
Sources: Yahoo UK.
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