Ramaphosa made the announcement from Tuynhuys in Parliament.
In his speech accepting the resignation, Mr Ramaphosa said that Mr Nene had "defended the cause of proper financial management and clean governance".
Nene's fall from grace came after he admitted to an anti-graft inquiry that he met members of the Gupta family at their home six times, contradicting statements in an earlier interview that he only encountered them at public events.
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.
The ANC forced Zuma to quit as president in February, clearing the way for his 65-year-old deputy and party leader Ramaphosa to take over.
"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. "I deeply regret these lapses and beg your forgiveness".
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.
Last week, Nene told an inquiry panel about the meetings he had held with the business family, a fact that he had earlier denied. Ramaphosa's spokeswoman Khusela Diko did not respond to phone calls. He is urging those ministers and other senior officials to follow Mr. Nene's example by volunteering to give testimony at the national inquiry into corruption so that their conduct can be reviewed.
Questions have also been raised about a PIC deal involving Nene's son, while he was chairman of the PIC.
Chawasema said the rand already started to firm ahead of the announcement‚ on rumours that Mboweni would be offered the job.
Announcing Nene's resignation on Tuesday, Ramaphosa said there had been for the past few days "quite a lot of discussion" that had arisen from Nene's testimony at the state capture commission.
Mboweni brings with him a wealth of experience, having headed the South African Reserve Bank for a decade until 2009.
Cabinet ministers must take a leaf out of former Finance Minister Nhlanhla Nene's book and resign if they have made a mistake, says Professor Jannie Rossouw, head of Wits School of Economics and Business Sciences.