The work from the artist's "double portrait" series was the most expensive artwork sold during Christie's 20th Century Week auctions in London.
Geldzahler was regarded one of the greatest curators of the 20th century, known for his work at the Metropolitan Museum of Art and as New York City Commissioner of Cultural Affairs.
The painting shows him alongside Scott, a painter and his then partner. It was painted at the time that Geldzahler was putting together his most famous exhibition, New York Painting and Sculpture: 1940-1970 at the Metropolitan Museum of Art, which marked the museum’s first exhibition of contemporary American art.
Hockney's 1972 work Portrait of an Artist (Pool with Two Figures) broke the world record for the most expensive work by a living artist sold at auction in November of last year.
The painting was sold as part of the Post-War and Contemporary Evening Auction, which totalled £79.2m and included works by Adrian Ghenie, Joan Mitchell, Gerhard Richter, Cecily Brown and Lucio Fontana.
Hockney's work is currently being exhibited alongside Van Gogh's at a show in Amsterdam, called Hockney – Van Gogh: The Joy of Nature.
The artist had to be rescued by firefighters after getting stuck in a lift with a number of journalists as he was trying to go outside for a cigarette, at an event in Amsterdam where he was speaking about the new exhibition.
He had earlier revealed his plans to visit his house in Normandy, which will be a new location and subject for his work.
“I can’t think of anything better in life than watching the spring happen in Normandy in 2019, I mean what better thing can I do. I can’t think of anything. Van Gogh would love it.”
He seemed unconvinced about the idea of returning to paint in Britain any time soon: “I think France is a lot more smoker friendly... I take that into consideration as well.”
The new Hockney show runs until 26 May.
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