"Portrait of an Artist (Pool with Two Figures)" was snapped up after more than nine minutes of bidding, dominated by two rival telephone bidders, AFP wrote.
The previous record was held by Jeff Koons and his ‘Balloon Dog (Orange),’ which sold for $58.4 million at Christie's in 2013.
It was standing room only in the packed sales room at Christie's in New York, where a smattering of applause broke out when the sale concluded, the painting hammering for $80 million.
The buyer's premium took the final price to $90,312,500, the auction house announced.
Christie's had estimated the 1972 oil painting at $80 million and called the Hockney ‘one of the great masterpieces of the modern era’.
"We rarely can say, 'This is the one opportunity to buy the best painting from the artist'," Ana Maria Celis, vice president of post-war and contemporary art at Christie's had said before the sale.
This is it.
In the picture, a smartly dressed man, standing on the edge of the pool, looks pensively at another figure swimming toward him in glistening waters, with an idyllic mountain view in the background.
The first man depicts Hockney's former lover and muse, Peter Schlesinger, who was one of his students at the University of California, Los Angeles.
The picture dates back to the year that their great love affair ended, and the swimmer could be Peter's new lover.
One of Hockney's most celebrated works, it has featured on the cover of a number of monographs about the artist and was part of an international retrospective that celebrated his 80th birthday in 2017.
Christie's declined to reveal the identity of the seller, but Bloomberg and the Artnet website have reported that it was owned by British billionaire Joe Lewis, who owns the Tavistock Group, London Premier League soccer team Tottenham Hotspur, and whom Forbes estimates to be worth $5 billion.
The Hockney had been taken on tour to drive up potential buyer interest, in Hong Kong, London and Los Angeles.
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 sales across rival houses offer a chance to see works often not viewed in public for decades and theatrical displays of purchasing power by a new generation of buyers, more international than ever.
The single most expensive piece of art ever sold at auction was the eye-watering $450.3 million paid for Leonardo da Vinci's ‘Salvator Mundi’ last year at Christie's in New York.