Nene was seen as one of Ramaphosa closest allies and a leading figure in the government's efforts to tackle graft that allegedly flourished under former president Jacob Zuma, who was ousted in February.
But Nene revealed to a judicial inquiry last week that he had met with the Gupta business family at their home and offices six times -- contradicting earlier statements that he had only met them in passing at social occasions.
"I have decided to accept his resignation," Ramaphosa told a televised press briefing in Cape Town.
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 reestablish public trust in government." Ramaphosa stressed that Nene "has not been implicated in any act of wrongdoing himself" and hailed him as minister who had "defended the cause of proper financial management as well as clean governance."
Nene, who was widely respected by investors, served as finance minister from 2014 to 2015 until he was sacked by Zuma and was re-appointed by Ramaphosa earlier this year.
Nene apologised after giving testimony to the inquiry, which is probing allegations of systematic corruption under Zuma's government involving the three Gupta brothers. "I was wrong in meeting the Guptas at their residence and not in my office or at least a public place," his public apology letter read.
"These visits do cast a shadow on my conduct as a public office bearer. I deeply regret these lapses and beg your forgiveness." Former central bank governor Tito Mboweni was named as Nene's successor.
Ramaphosa has vowed to crack down on corruption as he tries to revive the economy and boost declining support for the ruling ANC party ahead of elections next year.
At the graft inquiry, Nene accused Zuma of pushing policies designed to benefit the Guptas, including a massive nuclear power expansion programme.
Nene, speaking under oath at the hearings, also said that his then deputy Mcebisi Jonas was offered Nene's job after Nene refused to back the nuclear proposals.
The inquiry, which opened in August, is investigating allegations that Zuma organised a web of graft at government departments and public enterprises in a scandal known as "state capture".
South Africa, Africa's most advanced economy, slipped into recession in the second quarter of this year, and suffers a stubbornly high unemployment of about 28 percent.
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