Former central bank chief Tito Mboweni will take over from Nene.
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 said Nene wrote to him on Tuesday requesting to step down‚ and he had chose to accede to the request.
After leaving the Reserve Bank, Mboweni went into business, acting as an adviser in South Africa for Goldman Sachs Group and served as chairman of AngloGold Ashanti and on the boards of other companies.
Nene's departure from the finance portfolio comes as Treasury officials prepare to attend the International Monetary Fund's (IMF's) annual meeting in Bali and credit ratings agency Moody's is expected to do its next review of the country on Friday.
Mr. Nene had committed "errors of judgment" but was not personally implicated in any wrongdoing, Mr. Ramaphosa said in his announcement on Tuesday.
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Malema had threatened on Sunday that streets protests might be organised to demand for the removal of Nene as finance minister.
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.
While some lauded Nene for refusing to buckle while being pressurised to sign off on a nuclear deal Zuma wanted to get into with Russian Federation, as it had the potential to sink South Africa's already ailing economy.
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.
"This shouldn't really have much impact on the market or lead to any detrimental change to policy", Natalie Rivett, senior emerging-markets analyst at Informa Global Markets, said by phone from London.
Ramaphosa has made clean governance and the kick-starting of an economy mired in recession top priorities.
Nene's appointment to Ramaphosa's Cabinet this year was widely welcomed as a break from the alleged plundering of state resources.