"Salvator Mundi", which means "Savior of the World", went on public display in 2011 in a dramatic unveiling at The National Gallery in London, where the work was declared to be the first newly discovered Da Vinci painting in a century.
The French weekly Le Journal du Dimanche reported that two investment firms were behind the purchase as part of a financial arrangement involving several museums.
Christie's said the artwork will be going to the museum, but declined to say whether the Louvre Abu Dhabi bought the painting.
The young and dynamic crown prince, known by his initials MBS, used an intermediary to buy the much-sought-after painting of Christ, "Salvator Mundi", the newspaper reported, citing United States intelligence and other unnamed sources.
The New York Times reported Saudi Prince Bader bin Abdullah bin Mohammed bin Farhan al-Saud purchased the painting at the November 15 auction.
Abandoned and thought to be a fake for years, Leonardo's Da Vinci's masterpiece, "Salvator Mundi" hit Christie's auction block and shattered world records, raking in over $450 million.More news: South Shore now included in Winter Weather Advisory
The work was acquired by the Department of Culture and Tourism - Abu Dhabi for the museum.
Prince Bader has no history as a major art collector but is a friend and associate of Saudi Arabia's powerful Crown Prince Mohammed bin Salman, the Times said.
Arab leaders and kings, as well as French President Emmanuel Macron and his wife Brigitte, attended the museum's inauguration last month.
Here's where you'll be able to find the record-breaking Dhs1.65 billion work by da Vinci..
Interchange by Willem de Kooning-which changed hands privately in 2015-had also previously held the title of the painting with the highest known sale price, at US$300 million.
The painting, only recently rediscovered, was the last da Vinci left in private hands and fetched more than four times Christie's pre-sale estimate of about $100 million. It re-emerged in the 1950s, but was written off as a copy and sold for £45 or $60, according to CNN.