He will have to pay £157,750 overall including tax and commission.
The white bikini, which was expected to fetch more than £40,000, was sold as part of the largest auction of props and costumes used in 007 movies to date, featuring more than 250 lots.
It was bought by Planet Hollywood co-founder Robert Earl, who was bidding by telephone from his home in New York.
He said: "This is the most important piece of memorabilia ever sold at auction."
Celebrity couple Chris Evans and Billie Piper arrived at the Christie's auction halfway through the day - but left before the bikini went on sale.
They turned up after the sale of the 1965 Aston Martin DB5 driven by current Bond star Pierce Brosnan in the 1995 film GoldenEye.
The classic car, one of two used in a nail-biting chase sequence, fetched £140,000 - with buyer Max Reid asking for a vodka afterwards.
Mr Reid, 36, of Sheffield, who runs a computer leasing company, said: "Its 14 February and I thought it would make a great present for my wife."
He will have to pay £157,750 overall including tax and commission.
"I've not had a chance to phone her, so she's going to have a surprise when she watches the TV tonight," he told waiting camera crews.
He said he wanted to use it in promotions for his company, and he thought he'd picked up a bargain.
"It's gone cheap as far as these cars go - after all, it's a DB5 and it's appeared in a James Bond film," Mr Reid - who also has an Aston Martin DB7 - said.
He said he might bid for the bikini: "If it goes for a good price then why not. I want to put a bit of glamour back in to the computer business."
The Walther P99 stunt gun used by Brosnan in Tomorrow Never Dies fetched £8,000, while casino chips from The World is Not Enough fetched £1,400.
Classic moment
Ursula Andress's emergence from the sea in the 1962 film is now regarded as a classic moment in cinema and Bond history.
"My entrance in the film wearing the bikini on that beautiful beach made me world famous as 'the Bond girl'," said the Swiss actress.
The auction is the second sale of Bond memorabilia for Christie's.
A previous auction three years ago also captured huge public interest from collectors and fans around the world.
Wednesday's sale had been investigated by trading standards officers.
In a statement for BBC Breakfast News they had said they retained the right "to seize items or ask Christie's to withdraw them from the sale".