Zimbabwe's recently fired vice president is set to return to be sworn in as the country's new leader after Robert Mugabe announced his resignation in the middle of impeachment proceedings against him.

The state-run broadcaster reported that Emmerson Mnangagwa would arrive at a military air base in the capital Harare at 6pm (4pm GMT) on Wednesday, and the Parliament speaker said he would be sworn in Friday.

The swearing-in will take place at 10.30am at the 60,000 seat National Sports Stadium on the outskirts of Harare.

Zimbabweans erupted in response to Mr Mugabe's resignation on Tuesday, cheering and dancing in the streets late into the night, thrilled to be rid of a leader whose early promise after the end of white minority rule in 1980 was overtaken by economic collapse, government dysfunction and human rights violations.

Now the focus turns to Mr Mnangagwa, Mugabe's long-time deputy who was pushed aside earlier this month as unpopular first lady Grace Mugabe positioned herself to replace him and succeed her husband.

Mr Mnangagwa fled the country, claiming to have received threats on his life.

That led the military to step in a week ago, opening the door for the ruling party and the people to publicly turn against the president.

It is not clear what 93-year-old Mugabe and his wife will do next. Mugabe, who was the world's oldest head of state, said in his resignation letter that legal procedures should be followed to install a new president "no later than tomorrow".

Zimbabweans woke up to the first day in 37 years without Mugabe in power.

With some nursing hangovers, they looked over newspaper headlines such as "Adios Bob and Ta-ta President".

"I think this change of government is like a new breath of fresh air right across the country," said Patrick Musira on the streets of the capital, Harare.

"Everyone was engulfed with excitement and they are looking for a better future, a brighter future with work."

Zimbabwe's new leaders are faced with a once-prosperous nation whose economy has collapsed, sending well-educated but frustrated young people into desperate work as street vendors, while many have left the country.

Mr Mnangagwa is a former justice and defence minister who served for decades as Mugabe's enforcer, a role that earned him the nickname "Crocodile".

Many opposition supporters believe he was instrumental in the army killings of thousands of people when Mugabe moved against a political rival in the 1980s.

So far in the current political turmoil, Mr Mnangagwa has used inclusive language, saying in a statement hours before Mugabe's resignation that all Zimbabweans should work together to advance their nation.

"Never should the nation be held at ransom by one person ever again, whose desire is to die in office at whatever cost to the nation," Mr Mnangagwa said.