Mr Getty, the American oil heir who lives in Britain, had been upset by an allegation that his donation was motivated by a grudge against his father who died in 1976.
The Three Graces, by Antonio Canova, was bought by the Getty Museum in California for pounds 7.6m but an export licence has been delayed to see if British buyers can match the price.
The Getty Museum, one of the wealthiest in the world, is financed by a trust established by Mr Getty's father, and the V&A has three months left to beat its bid.
Timothy Clifford, director of the National Galleries of Scotland which joined the V&A in trying to keep the statue in Britain, made the comment about the family feud during interviews.
He made a public apology on Wednesday in which he admitted that he had no knowledge of the relationship between Mr Getty and his father.
Lord Armstrong of Ilminster, chairman of the board of trusteees of the V&A, said he was delighted at the news which meant the museum now had pounds 6.8m of the required pounds 7.6m.
'We hope that his generosity will encourage other benefactors and members of the public to help us in finding the amount we still need,' he said.
Mr Clifford said he was pleased by the decision. 'The National Galleries of Scotland are relieved, and above all, extremely grateful that Mr Getty has confirmed this generous donation.
'We shall continue our campaign to save the sculpture with renewed vigour, encouraged by Mr Getty's great generosity,' he said.
He refused to answer any further questions.
Mr Getty, 61, has lived in England since 1971 and used his wealth on earlier occasions to stop art treasures leaving Britain.Reuse content