Ramaphosa said Nene wrote to him on Tuesday requesting to step down‚ and he had chose to accede to the request.
There has been mixed reaction to Finance Minister, Nhlanhla Nene's confession around private meetings with the Gupta family at the compound in Saxonwold.
"We wish Minister Mboweni well as he journeys through the mammoth task of steering our economy in the right direction".
South African Finance Minister Nhlanhla Nene resigned on Tuesday after admitting that he met members of the powerful Gupta family, which is accused of corruption, BBC reported.
Nene has become a divisive figure after testimony he gave at an inquiry into allegations of corruption by the Guptas, in which he admitted to the previously undisclosed visits.
Both Zuma and the Guptas - who are at the heart of the inquiry into so-called "state capture" - have denied any wrongdoing.
After revealing the details of his own meetings, Mr Nene issued a public apology saying: "I am human too, I do make mistakes, including those of poor judgement".More news: China mum on Interpol chief Meng Hongwei's disappearance
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Former central bank governor Tito Mboweni was named as Nene's successor - the fifth finance minister in less than three years. "It is a measure of his character and his commitment to the national interest that he has taken this decision to resign in the wake of errors of judgment, even though he has not been implicated in acts of wrongdoing".
Asked repeatedly whether Nene still enjoyed his confidence and what the future might hold for the embattled finance minister, Ramaphosa made light of the questions and pretended there was something wrong with his hearing. The announcement led to a strengthening of the South African currency, the rand, which had weakened after earlier reports of Mr. Nene's likely resignation.
"What does this mean" about Minister Nene.
Apart from serving as Reserve Bank governor, Mboweni also served as labour minister under late president Nelson Mandela.
Mboweni clearly loves the social media platform, giving people a glimpse into his life, political thoughts and sense of humour.
Earlier on Tuesday, presidency spokesperson Khusela Diko said Ramaphosa had been engaging with Nene following his testimony at the state capture inquiry.