Emmerson Mnangagwa, who fled to South Africa two weeks ago, would also 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 was stepping down came in the form of a letter read out in parliament on Wednesday, abruptly halting impeachment proceedings against him.
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 that Mr Mnangagwa, 71, would serve the remainder of Mr Mugabe’s term until elections, which are due to take place by September 2018.
The state-run Zimbabwe Broadcasting Corporation (ZBC) confirmed that his swearing-in ceremony had been scheduled for Friday.
Nicknamed the “crocodile” due to 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.
His firing by Robert Mugabe two weeks ago triggered an unprecedented political crisis in the country.
It had been seen by many as an attempt to clear the way for Grace Mugabe to succeed her husband as leader and riled the military leadership, who stepped in and put Mr Mugabe under house arrest.
Under the constitution, the role of successor would normally go to the serving vice-president, Phelekezela Mphoko. However, Mr Mphoko – a key ally of Grace Mugabe – is not believed to be in the country, and there are reports that he has been fired by Zanu-PF.
Some have questioned whether the handover to Mr Mnangagwa will bring about real change in the country.
He was national security chief at a time when thousands of civilians died in post-independence conflict in the 1980s, though he denies having blood on his hands.
Opposition leader Morgan Tsvangirai told the BBC he hoped that Zimbabwe was on a “new trajectory” that would include free and fair elections.
He said Mr Mugabe should be allowed to “go and rest for his last days
Prominent opposition politician David Coltart tweeted: “We have removed a tyrant but not yet a tyranny.”
African Union president Alpha Conde said he was “truly delighted” by the news, but expressed regret at the way Mr Mugabe’s rule has ended.
“It is a shame that he is leaving through the back door and that he is forsaken by the parliament,” he said.
Celebrations in the streets
At 93, Mr Mugabe was – until his resignation – the world’s oldest leader. He once proclaimed that “only God” could remove him.
Lawmakers from the ruling party and opposition roared with glee, when the resignation letter was read aloud in parliament on Wednesday.
Driving through Harare, the cheers and the blaring of car horns signalled the end of the Mugabe era.
The man who dominated Zimbabwe for so long has already begun to fade into history here. It is a city singing with the noise of joy.
Exactly a week after the military first moved against President Mugabe, I was standing in parliament as legislators debated the motion to impeach him.
Suddenly, there was cheering.
An usher approached the speaker and handed him a letter. He stood to speak and we strained to hear his words. They were muffled but momentous. Robert Mugabe had resigned.
On the floor of the parliament I met jubilant MPs. Some danced. Celebrations spilled into the hallways and out into the street.