According to The New York Times, Mr Lauder paid $US135 million ($A183 million) for the gold-encrusted portrait of the wife of a Jewish sugar industrialist that had for decades been at the centre of a custody battle after being stolen by the Nazis.
Steven Thomas, a lawyer for Maria Altmann, a niece of Bloch-Bauer, would not give the price, citing a confidentiality agreement.
But he said it was "the most valuable painting ever sold".
The previous record price for a painting was $US104.1 million ($A141 million) for Pablo Picasso's 1905 "Boy with a Pipe" in a 2004 auction.
Mr Lauder purchased the Klimt portrait for his New York art gallery Neue Galerie New York, which focuses on German and Austrian decorative arts.
It is currently on show at the Los Angeles County Museum of Art (LACMA).
It is not known if any collector has paid more for a work on the private market.
Portraits fetch millions
Elsewhere, a Modigliani portrait of his muse Jeanne Hebuterne was sold for 16.3 million pounds ($A41 million) at a London auction of impressionist and modern art.
The 1919 portrait of his common-law wife, entitled Jeanne Hebuterne (au chapeau), was painted a year before the death of the Italian painter and sculptor Amadeo Modigliani.
Edgar Degas's 1895 La Sortie du Bain, an 1895 pastel of a woman bathing, her face hidden by a raised arm, which once belonged to Bob Guccione, founder of the soft-core Penthouse magazine, was sold for 6.78 million pounds ($A17 million) at the same auction.
During the sale, which ends tomorrow, the London auction house Sotheby's hopes to pull in some 115 million pounds ($A289.6 million).
A Gabonese tribal mask was sold at auction on Paris on Saturday for 5.9 million euros ($A10.14 million), a record price for tribal art.
Last week the auction in the French capital of a spectacular private collection of Art Deco furniture and art objects smashed records and raised nearly 60 million euros ($A103 million).
On June 5, a watercolour by the British landscape artist JMW Turner flew the flag for 19th century artists, breaking the world record for a British watercolour when it sold for nearly $US11 million ($A14.93 million) at auction.
Battle for Klimt
The Klimt painting was the subject of a restitution battle between the Austrian government and Maria Altmann, who argued that it was seized along with the four other Klimt paintings by the Nazis in World War II.
In January, a US court awarded the five paintings to Ms Altmann, 90, and other relatives.
Viennese art collectors on Monday lamented the sale and criticised the Austrian authorities for failing to keep the painting in the country.
"If the (Austrian) authorities had been more skilful, Austria would have been able to obtain the portrait for free," said Rudolf Leopold, director of the largest modern art museum in Austria.
Mr Leopold, himself a big collector of Klimt and his pupil Egon Schiele, said "Mr Lauder paid too much" for the picture.
There was also disappointment in Los Angeles at the sale.
The Los Angeles Times said the price Mr Lauder paid is "believed to be what LACMA had on the table for all five Klimt paintings in its show," it added.
However Ms Altmann said the family was "thrilled with this result".
“It fulfils our wish that all five paintings be seen by a large American audience, first in Los Angeles and now in New York.”
Mr Lauder, who has a fortune estimated at $US2.8 billion by Fortune magazine, was the US ambassador to Vienna in 1986-87 and has a major collection of Klimt and Schiele works.
Klimt (1862-1918) gained considerable acclaim with his portraits of the Vienna upper classes, particularly women.
His work was often criticised at the time for being too erotic but now it is internationally acclaimed.