Inspired by the lily pond in Monet's garden at Giverny in France, the painting was the top lot at Sotheby's sale of modern and impressionist works.
It totalled just under £122m, including £15.2m for Piet Mondrian's 1927 Composition with Red, Blue and Grey.
Sotheby's said it proved collectors are still keen to acquire "trophy art".
Paintings by Sisley, Picasso, Manet and Kandinsky were also among the 46 works, with only four pieces failing to find buyers as many sold close to the top end of the pre-auction estimates and sometimes above.
"The Nympheas selling for such a huge sum is again a reflection that this is still a market that is driven by trophies, that the great works by the major masters are still really sought after," said Philip Hook from Sotheby's.
The auction house said the bidding for the Monet work attracted buyers from Asia and all over the world and went on for 10 minutes, going up in £250,000 increments in its final stages.
It said the painting, from the "most iconic and celebrated of Monet's painting series, can be counted among the artist's greatest achievements".
It once belonged to Paul Durand-Ruel, the legendary art dealer who championed the Impressionists and represented Monet.
The same work had been offered for auction in 2010 but failed to reach its reserve price. Sotheby's said this time it had carried a more "realistic" estimate of £20m to £30m.
The sale price of £31.7m included a buyer's premium.
Two other Monet paintings were also offered in the sale, La Seine a Argenteuil which sold for £8.5m and Antibes, vue du plateau Notre-Dame, which sold for £7.9m.

The 48-year-old took had been in charge of Posh since replacing Dave Robertson in September and lifted the club as high as the play-off places in January.
But they have since fallen to 14th in the table and have lost four of their last five matches.
Assistant Grant McCann will take charge for the final two games of the season.
Westley was asked by BBC Radio Cambridgeshire if he felt increased pressure following Saturday's defeat and said: "I come to work every day and feel pressure, I put pressure on myself.
"I don't like losing football matches, but I know the job here. The job is to build long-term winning.
"Right now the job is to get our young players on the pitch, to give them a chance to succeed and to grow, and that's what we've done (against Scunthorpe).
"There'll be lessons learned by all of the players, and if we're going to be a successful club next year, then we need the young players to step up to the plate and the experience now will be useful for them."
The former Stevenage and Preston boss began his career at the ABAX Stadium with 10 wins from his first 14 matches in all competitions.
However, after losing to West Brom in a FA Cup fourth-round replay on penalties and the January sale of forward Conor Washington, still the club's top scorer this season with 15, Posh lost six of their next seven league matches.
After a brief run of three straight victories, the club's form dipped again, leading chairman Darragh MacAnthony to say "I employ over 300 people at Peterborough United, not one of those employees right now has a job in the summer".
Earlier this week, Westley also bemoaned his side's poor discipline - the worst record in the Football League with 104 yellow cards and seven reds - saying it was costing them games.
A brief statement on the Peterborough website read: "The club would like to thank Graham for his efforts on behalf of the football club.
"Chairman Darragh MacAnthony will take time to speak to prospective candidates for the vacant manager position."
A 1906 Claude Monet water lilies painting, Nympheas, has sold for £31.7m in London, the second highest price ever paid for the artist at an auction.
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League One side Peterborough United have parted company with manager Graham Westley following Saturday's 2-0 defeat by Scunthorpe United.