The 93-year-old, who has also been assured safety in his home country, told negotiators he wanted to die in Zimbabwe and had no plans to live in exile, the government source said.
"It was very emotional for him and he was forceful about it," they said.
"For him it was very important that he be guaranteed security to stay in the country... although that will not stop him from travelling abroad when he wants to or has to."
Mr Mugabe led Zimbabwe from independence in 1980 but stepped down on Tuesday after the army seized power and the ruling party turned against him.
Emmerson Mnangagwa, the former vice president, will be sworn in as president on Friday.
He has urged his citizens to be peaceful and desist from any form of "vengeful retribution."
On Wednesday night, he greeted a cheering crowd outside the ruling party headquarters and promised "a new, unfolding democracy." He also reached out to the world, saying international help is needed to rebuild the shattered economy.
Mr Mnangagwa, a former justice and defence minister with close ties to the military, served for decades as Mr Mugabe's enforcer, a role which earned him the nickname "Crocodile."
Many opposition supporters believe he was instrumental in the army killings of thousands of people when Mr Mugabe moved against a political rival in the 1980s.
The 75-year-old said he had received messages of support from other countries.
"We need the cooperation of the continent of Africa," he said. "We need the cooperation of our friends outside the continent."
After meeting with South Africa's president, Mr Mnangagwa flew home in a private jet. He said his inauguration on Friday is "when we finish this job to legally install a new president."
He will serve Mr Mugabe's remaining term until elections at some point next year after the ruling party's Central Committee voted to remove Mr Mugabe from his party leadership post.
According to protocol, Zimbabwe's outgoing leader would attend the swearing-in of Mr Mnangagwa.
But while Mr Mugabe remains in the capital, Harare, it is not clear whether he will attend the ceremony.
Additional reporting by agencies
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