The 507-carat gem is one of the largest diamonds ever discovered.
Petra, the mining company that discovered the diamond, said the price reflected the gem's rare combination of size and exceptional clarity.
"It has the potential to produce one of the world's most important polished gems," said Petra's chief executive Johan Dippenaar.
It is not known what the buyer - the Chow Tai Fook Jewellery Company - plans to do with the diamond.
The diamond was found at the Cullinan mine in South Africa - a known source of some of the world's largest diamonds.
A 168-carat stone was also discovered along side it, as well as one of 58 carats and another of 53 carats.
The largest diamond to be discovered, named the Cullinan, was 3,106 carats.
It was cut into nine separate stones, some of which form part of the British Crown Jewels.