Public Protector Thuli Madonsela, the country's ombudswoman, ruled in 2014 that Zuma and his family had "benefited unduly" from the work on Zuma's rural residence of Nkandla.
Among the supposed security upgrades were a swimming pool described as a fire-fighting facility, a chicken run, a cattle enclosure, an amphitheatre and a visitors' centre.
"To achieve an end to the drawn-out dispute ... The President proposes that the determination of the amount he is to pay should be independently and impartially determined," said a presidential statement.
Zuma had previously denied any wrongdoing over the upgrades, with opposition lawmakers often disrupting his parliamentary address by chanting "Pay back the money!"
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His change of position came ahead of Constitutional Court hearing next week as opposition parties the Democratic Alliance and Economic Freedom Fighters (EFF) unite in a legal bid to force him to refund the cash.
The upgrades were valued in 2014 at about 216 million rand (then worth USD 24 million, 22 million euros).
The statement stressed that Zuma "remains critical of a number of factual aspects and legal conclusions" contained in the damning public ombudsman report.
He will make his annual state of the nation address in parliament next Thursday.
The occasion descended into chaos last year when EFF lawmakers scuffled with security after interrupting him to protest over the Nkandla scandal.