"Get ready for your first cabinet meeting tomorrow!"
He added that Nene feared his testimony to the inquiry "detracted from the important task of serving the people of South Africa particularly as we work to re-establish public trust in government".
Ramaphosa said he had received a resignation letter from Nene and had made a decision to accept it.
This, on the back of Nene's appearance before the state capture commission of inquiry last week, during which he admitted visiting the Gupta family on numerous occasions between 2009 and 2014.
The visits occurred when he was deputy finance minister and also finance minister before Zuma fired him from that post in December 2015, Nene testified.More news: Trump lashes out at Capitol Hill protesters
He said no person should be above scrutiny and all relevant and credible accusations of wrongdoing should be thoroughly investigated. "I deeply regret these lapses and beg your forgiveness".
But Nene's confession at the inquiry came as a surprise, as he had previously denied meeting with the politically connected family, telling eNCA in April 2016 that he had only seen them during "public gatherings".
Political parties have rejected Nene's apology. Five months after refusing to sign a letter of guarantee that would have given the project to Russia's state-controlled nuclear energy company, Mr. Nene was sacked from Mr. Zuma's cabinet and was briefly replaced by a pro-Gupta minister.
In a separate issue, a South African newspaper reported last week that Mr. Nene's son, Siyabonga Nene, had sought financing from a state agency, the Public Investment Corporation, at a time when his father was the senior government representative on the PIC board.
The rand firmed, moments before Mboweni, was announced Finance Minister at a ceremony in Cape Town. The Guptas have been accused of having improper influence over former president Jacob Zuma and his executive, as well as control of operations at state owned enterprises, which they used to loot billions of rand from South African taxpayers.
"Mboweni possesses the necessary integrity, skills set and experience which can generate confidence in the markets, among investors and generally in the business community", said Raymond Parsons, a professor at the North West University's School of Business and Governance.