He reveals he told the 93-year-old that the current constitutional crisis was a matter between the people of Zimbabwe and him, rather than a spat between Mnangagwa and Mugabe.
Parliament speaker Jacob Mubenda gave permission for a joint session of the House of Assembly and the Senate to debate a motion that would trigger impeachment proceedings against Mugabe.
Zimbabwe's army addressed the country on state-run media on November 15, vehemently denying speculation this was a coup d'etat and assuring citizens the president and his family are "safe and sound". Mnangagwa, a former security chief known as The Crocodile, is expected to take over as president.
People celebrate in the streets of Harare after the resignation of Robert Mugabe.
British Prime Minister Theresa May said the resignation of President Robert Mugabe on Tuesday has given Zimbabwe "an opportunity to forge a new path free of the oppression that characterised his rule".
My decision to resign is voluntary on my part and arises from my concern for the welfare of the people of Zimbabwe and my desire to ensure a smooth, peaceful and non-violent transfer of power that underpins national security, peace and stability.
Zimbabwe's military is believed to have taken charge of the country earlier this month.
"We are just so happy that things are finally going to change", Togo Ndhlalambi, a 32-year-old hairdresser, told AFP.
At least a semblance of legitimacy - especially for a government under Mnangagwa, who is known as the enforcer of some of Mugabe's most ruthless policies - will be critical in gaining recognition from regional powers, Western governments and worldwide lenders.
His grip on power was shattered last week when armoured military vehicles took to the streets, blockaded parliament and placed the president under house arrest in an operation that had all the hallmarks of a coup.
His comments could be interpreted as referring to Mugabe's wife, Grace, whose lavish lifestyle and political ambitions alarmed sections of the ruling party's elite.
The chief whip of ruling party Zanu-PF, Lovemore Matuke, told Reuters that Mr Mnangagwa would serve the remainder of Mugabe's term.
Mnangagwa's whereabouts unknown: The former vice president's statement offered no clues about his location.
- August 1996: Mugabe marries his former secretary Grace Mufuru. Grace has not been seen since the start of the crisis.
The prospect of a dynastic succession alarmed the military, which confined Mr Mugabe to his home last week and targeted what it called "criminals" around him who allegedly were looting state resources - a reference to associates of the first lady.
Before the resignation, crowds rallied outside parliament, dancing and singing.
The demonstrations drew citizens of all ages and races, jubilant that Mugabe's fate had been sealed. Pressure from within the country and from overseas had been building on Mugabe to resign, but observers had warned that the country might have to brace itself for lengthy impeachment proceedings.