The painting is known as Salvator Mundi (Saviour of the World).
It is the highest auction price for any work of art and brought cheers and applause at the packed Christie's auction room.
Leonardo da Vinci died in 1519 and there are fewer than 20 of his paintings in existence.
Salvator Mundi, believed to have been painted sometime after 1505, is the only work thought to be in private hands.
Bidding began at $100m and the final bid for the work was $400m, with fees bringing the full price up to $450.3m. The unidentified buyer was involved in a bidding contest, via telephone, that lasted nearly 20 minutes.
The painting shows Christ with one hand raised, the other holding a glass sphere.
In 1958 it was sold at auction in London for a mere £45 at auction in London. By then the painting was generally reckoned to be the work of a follower of Leonardo and not the work of Leonardo himself.
BBC arts correspondent Vincent Dowd says that even now attribution to Leonardo is not universally accepted.
One critic has described the surface of the painting to be "inert, varnished, lurid, scrubbed over and repainted so many times that it looks simultaneously new and old".

"Any private collector who gets suckered into buying this picture and places it in their apartment or storage, it serves them right," Jenny Saltz wrote on Vulture.com.
But Christie's has insisted the painting is authentic and billed it as "the greatest artistic rediscovery of the 20th Century".
When Salvator Mundi re-emerged from obscurity in 2005, it created huge public interest as a "lost Leonardo".

Salvator Mundi - Leonardo da Vinci's 'mysterious masterpiece'
 The painting was sold by the family trust of the Russian billionaire collector Dmitry E Rybolovlev, who is reported to have bought it in a private sale in May 2013 for $127.5m (£98m)
 It apparently once belonged to King Charles I of England in the 1600s and was "rediscovered" in 2005
 Dr Tim Hunter, who is a specialist in Old Master and 19th Century paintings, says it is "the biggest discovery of the 21st Century"
 The painting has had major cosmetic surgery - its walnut panel base has been described as "worm-tunnelled" and at some point it seems to have been split in half - and efforts to restore it resulted in abrasions

Other high-priced paintings

1. Interchange by Willem de Kooning - $300m (£230m)
The 79 x 69 inch (2 x 1.75m) expressionist piece was painted in 1955. It was sold to hedge-fund founder Kenneth C. Griffin, who spent about $500m in total in 2016 on a Pollock piece too.
2. Nafea Faa Ipoipo (When Will You Marry?) by Paul Gauguin - $300m (£230m)
His post-impressionist painting of Tahiti women was sold in February 2015 to a mystery buyer, rumoured to be a Qatari museum, and is thought to share the top spot with a piece by William de Kooning.
3. The Card Players by Paul Cézanne - $250m (£190m)
This sale to Qatar broke records in 2011. The piece was painted at the end of the 19th Century and was part of a five-part series. The others in the series are at some of the world's most prestigious art museums including the Metropolitan Museum of Art in New York.
4. Number 17A by Jackson Pollock - $200m (£150m)
This abstract expressionist piece was also sold in 2016 to Kenneth C. Griffin from American businessman David Geffen.

Source: BBC