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, which did not immediately identify the buyer.
The highest price ever paid for a work of art at auction had been 179.4 million US dollars (£136 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 US dollars (£227 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 dollars (£75 million), the opening bid of the auction, which ran for 19 minutes. The price hit 300 million US dollars about halfway through the bidding.
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 US dollars (£7,600). The art dealers restored the painting and documented its authenticity as a work by Leonardo.