President Cyril Ramaphosa said he accepted the resignation “in the interests of good governance”.
The Guptas have been accused of working with former President Jacob Zuma to secure government contracts and determine cabinet appointments.
Both the Guptas and Mr Zuma deny the allegations
Last week, Nene confessed to meeting with members of the Gupta family six times at their residence, after previously denying these meetings.
Nene will be replaced by Tito Mboweni, who previously held the post of governor of the SARB.
He apologised for his actions and handed his letter of resignation to Ramaphosa.