Robert Mugabe resigned as Zimbabwe's president on Tuesday, shortly after parliament began an impeachment process to end his nearly four decades of rule.

The 93-year-old clung on for a week after an army takeover and expulsion from his own ruling ZANU-PF party, which also told him to leave power.

"I Robert Gabriel Mugabe in terms of section 96 of the constitution of Zimbabwe hereby formally tender my resignation... with immediate effect," said parliament speaker Jacob Mudenda, reading the letter.

The letter did not, however, mention who he was leaving in charge of the country. The speaker added he was working on legal issues to make sure a new leader was in place by the end of Wednesday.

The bombshell news was delivered to a special joint session of parliament.

People danced and car horns blared on the streets of Harare at news that the era of Mugabe - who has led Zimbabwe since independence in 1980 - was finally over.