President Emmerson Mnangagwa, a former loyalist, was sworn in on Friday and attention is focused on whether he will name a broad-based government or select figures from Mugabe's era.
The Standard newspaper quoted sources within Mr Mugabe's inner circle as saying the devout Catholic held a rosary as he told his close associates and a team of negotiators at his 'Blue House' Harare mansion that he was resigning. He announced the decision as parliament heard a motion to impeach him.
"He looked down and said 'people were chameleons'," one of the sources was quoted as saying.
The state-owned Sunday Mail quoted Father Fidelis Mukonori, a Jesuit priest who is a close friend of Mr Mugabe and mediated his resignation with the military, as saying Mr Mugabe's face "just glowed" after he signed the resignation letter.
"So we are not talking about a bitter man. I told him that it was good for him to see someone running the country," Mukonori told the Sunday Mail.
Neither Father Mukonori nor Mr Mugabe's close aides were immediately available for comment.
Mr Mugabe's fall after 37 years in power was spurred by a battle to succeed him that pitted Mr Mnangagwa, who had stood by him for 52 years, and Mr Mugabe's wife Grace, who is 52.
The privately-owned Standard newspaper, which has been critical of Mr Mugabe and his government over the years, urged Mr Mnangagwa to "walk the talk on graft".
The new government is already moving to bring some of Mr Mugabe and his wife's close associates to book and former finance minister Ignatius Chombo was in court on Saturday on corruption charges.