The buyer's premium of the portrait took the final price to $90,312,500, the auction house announced.
The previous record was held by Jeff Koons' Balloon Dog, which sold for $US58.4 million ($80.2 million) in 2013.
Christie's did not identify the seller or the successful bidder, who was bidding via telephone during a almost 10-minute contest for the work.
It was standing room only in the packed sales room at Christie's in NY, where a smattering of applause broke out when the sale concluded, the painting hammering for $80 million.
The Hockney painting is not the only one making news this week.
The artwork depicts two men at a pool with lush mountains in the backdrop.
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It features the lyrics, "I believe you and me are sisters and brothers/And I believe we're made to be here for each other". Kacey Musgraves, the only woman nominated for album of the year, won the prize for " Golden Hour ". "God bless you all".
The painting was destroyed a few months later but the idea stuck with the Bradford-born artist, who revisited the concept a year later, when he travelled to Saint-Tropez in the south of France with a friend to stage photographs.
He began a new work that cast his former lover and favourite muse, California artist Peter Schlesinger, as a young man looking down at a swimming figure.
Other sale highlights included Francis Bacon's "Study of Henrietta Moraes Laughing", which sold for $21.7 million against a pre-sale estimate of $14 million to $18 million, and Alexander Calder's "21 Feuilles Blanches", which more than doubled its high estimate, selling for just under $18 million.
Thursday's sale at Christie's flagship post-war and contemporary evening art sale caps the end of the biannual marquee art auctions held every year in November.
The most expensive work of art by a living artist is now a painting by out artist David Hockney.