The 1907 gold-flecked painting, one of the most recognisable artworks of the 20th century, was bought by US cosmetics magnate Ronald S Lauder, who described it as a "once in a lifetime acquisition".
It is thought to be the highest price paid for a painting. The previous record was $104.1m for Pablo Picasso's Boy with a Pipe.
The work - a portrait of Adele Bloch-Bauer, the wife of a Jewish sugar industrialist - was sold by Bloch-Bauer's niece, Maria Altmann, and her family, her lawyer told The New York Times newspaper.
It was the focus of a fierce battle between the Austrian government and Altmann, who said it had been stolen along with four other Klimt paintings by the Nazis during World War Two, the paper reported.
Klimt, born near Vienna, Austria, in 1862 and a prominent member of the Art Nouveau movement, was considered one of the finest European painters working at the turn of the century.
He died of a stroke in 1918.
Altmann said the paintings had been taken from her uncle's estate by the Nazis after he fled Vienna in 1938.
In his will, he had bequeathed them to Altmann and her two siblings, she said.
"Mr Lauder has a great understanding of Austria and a great love for Klimt"
Maria Altmann, the painting's former owner
However, lawyers in Austria said that Altmann's aunt, who died of meningitis in 1925, had willed the paintings to the government gallery.
Altmann and her family responded by suing the Austrian government in the US. The case ultimately reached the US supreme court, which ruled in Altmann's favour.
In January, all five paintings were awarded to Altmann, now 90 years old and living in Los Angeles, and other members of her family.
Altmann told the newspaper that she had met the painting's buyer, Lauder, and had appreciated his concern for the painting's fate.
"Mr Lauder has a great understanding of Austria and a great love for Klimt," she said.
The paintings will be displayed in Lauder's Neue Galerie art museum in New York from July 13 to September 18.