The Farnese Blue was given as a wedding present to Elizabeth Farnese, daughter of the Duke of Parma, when she married Philip V of Spain in 1715.
It then passed down through the generations, moving from Spain to France, Italy and Austria.
The 6.1 carat diamond comes from the famous Golconda mine of India.
It sold after just four minutes of bidding at Sotheby's, easily passing the auction house's estimate of $3.5m-$5m.
"We were expecting a good result but we started from $3.5m and we ended up with $6.7m, so we exceeded our expectation," said Sotheby's jewellery specialist, Daniela Mascetti.
"Good jewels, well-designed, well-made, with a signature, with a perfect... slot in time, in age, do very well."
According to the auctioneers' website, the pear-shaped diamond once formed part of a tiara owned by the ill-fated French Queen Marie Antoinette.
The identity of the new owner has not been revealed.
BBC
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