"After due consideration of the circumstances around this matter and in the interest of good governance, I have made a decision to accept his resignation", said Ramaphosa.
The party said it "noted" Tito Mboweni's appointment as finance minister and called on him to prioritise the needs of South Africans, especially the poor.
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.
He then added that that Nene can no longer inspire much needed confidence to revive the economy.
Both Zuma and the Guptas - who are at the heart of the inquiry into so-called "state capture" - have denied any wrongdoing.
Rumours of his intended resignation on Monday led to a fall in the value of South Africa's currency, the rand, but it has since recovered its value.
Mr Nene, 59, was deputy finance minister and head of the Treasury at the time of the meetings at the Guptas' property in Johannesburg between 2009 and 2014.
Senate summary of Kavanaugh FBI report reveals ten people agents spoke to
Under new rules approved past year , 50 votes are needed for victory in Friday's procedural vote. A major procedural vote in the Senate, which the GOP controls 51-49, is planned for Friday.
Jonas, a former deputy finance minister, was offered the post on Monday, according to the people, who spoke on condition of anonymity because they aren't authorized to comment.
In December 2015, Zuma fired Nene and replaced him with little unknown ANC MP Des van Rooyen. "I am human too, I do make mistakes, including those of poor judgement", Nene said.
In a nationally televised address, Ramaphosa said he accepted Nene's resignation because of "errors of judgment" as a result of a controversy surrounding Nene's testimony in an ongoing graft inquiry in South Africa.
A senior government official told News24 the reports were true and that the conversation took place telephonically, but refused to divulge any further information and instead directed questions to the Presidency and Nene.
The ANC forced Zuma to quit as president in February after nearly nine years in office, clearing the way for his 65-year-old deputy and party leader Ramaphosa to take over.
"Under hard circumstances and often under great pressure‚ he consistently defended the cause of proper financial management and clean governance".