In 2014, a report by the public protector said Mr Zuma had “benefited unduly” from the upgrades.
Mr Zuma said the auditor-general and finance minister should determine how much he should repay to end the dispute.
The announcement comes a week before a constitutional hearing on the matter.
The refurbishment of the residence in the village of Nkandla, in Mr Zuma’s home province of KwaZulu-Natal, has turned into a major political controversy in South Africa.
Some of of the money was spent on building an amphitheatre, swimming pool, and cattle enclosure.
The opposition Democratic Alliance (DA) and Julius Malema’s Economic Freedom Fighters (EFF), who have called for a corruption investigation, say they are pressing ahead with their court case regardless of the president’s latest offer.