According to BBC, Emmerson Mnangagwa, who fled to South Africa two weeks ago, would fly home on Wednesday, it added.
His dismissal led the ruling party and the military to intervene and force an end to Mr Mugabe's 37-year long rule.
The news sparked wild celebrations across the country late into the night.
The announcement that the 93-year-old president was stepping down came in the form of a letter read out in parliament on Wednesday, abruptly halting impeachment proceedings against him. BBC reports.
In it, Mr Mugabe said he was resigning to allow a smooth and peaceful transfer of power, and that his decision was voluntary.A spokesman for the ruling Zanu-PF party said Mr Mnangagwa, 71, would serve the remainder of Mr Mugabe's term until elections that are due to be held by September 2018.
The state-run Zimbabwe Broadcasting Corporation (ZBC) confirmed that his swearing-in ceremony had been scheduled for Friday.
Nicknamed the "crocodile" because of his political cunning, Mr Mnangagwa issued a statement from exile calling on Zimbabweans to unite to rebuild the country.
"Together, we will ensure a peaceful transition to the consolidation of our democracy, and bring in a fresh start for all Zimbabweans and foster peace and unity," Mr Mnangagwa told Zimbabwe's NewsDay on Tuesday.
Mr. Mnangagwa's firing by Robert Mugabe two weeks ago triggered an unprecedented political crisis in the country.