Garry Weston, 72, the chairman of Associated British Foods plc, gave the money for the museum's Great Court Scheme, a restructuring and reorganisation of the London site. The gift has pushed the museum fund-raising beyond its target of pounds 97.9m.
Mr Weston, whose personal wealth is estimated at pounds 1.5bn, said it was also the biggest donation the charitable Garfield Weston Foundation had made.
"We recognise the outstanding quality of the Great Court scheme and its vital importance to the future of our national museum, the great museum of world culture," he added.
Gerard Vaughan, the director of the British Museum Development Trust, said he was amazed by the generosity.
"Two years ago Mr Weston gave us pounds 10m anonymously and more recently it came to his attention that we were into the final phase of fund-raising and we had pounds 10m to go. He said because the foundation had started the donations for the project they would like to finish it off and gave us another pounds 10m."
The Great Court scheme, part of a project that includes restoration of the museum's famous Round Reading Room, is to open in November 2000.
Associated British Foods owns Twinings Tea, Silver Spoon sugar and Kingsmill bread. Mr Weston has been the chairman and chief executive since 1967 and his family owns two-thirds of the firm. Last month they received a pounds 300m payout from the sale of the Irish retailing businesses to Tesco several years ago and in 1998 they got nearly pounds 50m.
Late last year Mr Weston announced that he would retire as chief executive in June but will continue as chairman. It has been suggested that this decision was made to avoid a succession battle between his three sons, who all hold senior positions in the business.
Despite his enormous wealth, Mr Weston is happy to spend the weekend fixing the lawnmower and he often travels to work on public transport. His car is a second-hand Mercedes that was going spare after a senior executive was made redundant.
Fiona Foster, administrator of the Garfield Weston Foundation, said: "They are a very modest family and they do not seek publicity.
"They support a wide range of charitable activities including the arts and are very pleased to support significant projects like these."
The Garfield Weston Foundation was established in 1958 and endowed by Mr Weston's father Willard Garfield and two generations of the family. Its income has grown from pounds 118,000 in 1960 to approaching pounds 30m in the current year, in parallel with the growth of Associated British Foods.
Mr Weston was born in Canada, the fourth of nine children, and came to Britain in 1931. It was while running the family bakery in Slough in the 1950s that he hit upon the idea of the Wagon Wheel biscuit after staff complained they were not making anything new.
nTwo men have been arrested over a pounds 1m armed robbery of an art gallery. About 50 police, some armed, raided an industrial estate in Rotherham, South Yorkshire. All 20 paintings taken from York City Art Gallery in January, including an 1820s Turner watercolour, were recovered. The museum curator, Richard Green, said: "They are in good condition given what they have been through, much better than we expected."
The men, aged 29 and 49, from Rotherham, are being held for questioning.