The gift leaves Britain only pounds 800,000 short of the pounds 7.6m bid by the Getty Museum for the statue by Antonio Canova, with three months to raise the difference.
Mr Getty, who inherited a quarter of the dollars 1.3bn ( pounds 870m) Getty Trust when his father died in 1976, is known as an Anglophile and benefactor of the arts - most notably for his gift of pounds 50m for the National Gallery extension.
Timothy Clifford, director of the National Galleries of Scotland, which approached Mr Getty last week, said: 'I think Getty never got on at all well with his father. That is the crucial point of it.'
But he added: 'He greatly admires this piece of sculpture and sees what a plight we are in. He is immensely good as a benefactor. He has a wonderful track record of generosity, particularly as far as the visual arts are concerned.'
Mr Getty lives in a country house in Buckinghamshire, with an adjoining castle to house his collection of medieval manuscripts. Although still a US citizen, he has lived in England since 1971, and was given an honorary knighthood for his donations to the arts.Reuse content