According to the New York Times, the buyer is a little-known prince from Saudi Arabia. Prince Bader bin Abdullah bin Mohammed bin Farhan al-Saud is not expected to keep the art at his home. Instead, it will go in the new branch of the Louvre at Abu Dhabi.
The sale of the painting of Christ smashed previous records for artworks sold at auction or privately.
The painting, called "Salvator Mundi," Italian for "Savior of the World," is one of fewer than 20 paintings by Leonardo known to exist and the only one in private hands. It was sold by Christie's auction house.
"'Salvator Mundi' is a painting of the most iconic figure in the world by the most important artist of all time," said Loic Gouzer, co-chairman of post-war and contemporary art at Christie's. "The opportunity to bring this masterpiece to the market is an honor that comes around once in a lifetime."
The highest price ever paid for a work of art at auction had been $179.4 million, for Pablo Picasso's painting "Women of Algiers (Version O)" in May 2015, also at Christie's in New York. The highest known sale price for any artwork had been $300 million, for Willem de Kooning's painting "Interchange," sold privately in September 2015 by the David Geffen Foundation to hedge fund manager Kenneth C. Griffin.
A backer of the "Salvator Mundi" auction had guaranteed a bid of at least $100 million. The bidding opened at $75 million and ran for 19 minutes. The price hit $300 million about halfway through the bidding.
People in the auction house gallery applauded and cheered when the bidding reached $300 million and when the hammer came down on the final bid, $400 million. The record sale price of $450 million includes the buyer's premium, a fee paid by the winner to the auction house.
"We are extremely pleased with the record-breaking result for this remarkable and historical work," Gouzer said.
The 26-inch-tall Leonardo painting dates from around 1500 and shows Christ dressed in Renaissance-style robes, his right hand raised in blessing as his left hand holds a crystal sphere.
Its path from Leonardo's workshop to the auction block at Christie's was not smooth. Once owned by King Charles I of England, it disappeared from view until 1900, when it resurfaced and was acquired by a British collector. At that time it was attributed to a Leonardo disciple, rather than to the master himself.
The painting was sold again in 1958 and then was acquired in 2005, badly damaged and partly painted-over, by a consortium of art dealers who paid less than $10,000 (8,445 euros). The art dealers restored the painting and documented its authenticity as a work by Leonardo.
The painting was sold by Russian billionaire Dmitry Rybolovlev, who bought it in 2013 for $127.5 million in a private sale that became the subject of a continuing lawsuit.
Christie's said most scholars agree that the painting is by Leonardo, though some critics have questioned the attribution and some say the extensive restoration muddies the work's authorship.
(The Associated Press contributed to this report)