But Zanu-PF legal secretary Patrick Chinamasa told Reuters news agency that Mr Mnangagwa would be sworn in on Wednesday or Thursday.
Notes of caution
Despite welcoming the news, Zimbabwean opposition and civil society figures have warned that the political culture needs to change.
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 Zimbabwean opposition politician David Coltart tweeted: "We have removed a tyrant but not yet a tyranny."
Both Robert and Grace Mugabe, 52, are believed to still be at a mansion in Harare.
Robert Mugabe - Timeline of a political life