Half of the proceeds - $3.8m - will be used to fund infrastructure projects to benefit the community of the small village where it was discovered.
The Sierra Leone government rejected a bid of $7.8m at an earlier auction.
The government is now expected to use the money raised to improve conditions in the village of Koryardu, including the introduction of a fresh supply of water, electricity, roads, medical care and the building and maintenance of schools.
"The Peace Diamond bought by Laurence Graff will change lives even though it's a shame the diamond hasn't sold for a wildly expensive price," the managing director of 77diamonds.com, Tobias Kormind, said.
An earlier bid of $7.8m was rejected by the government when the stone was initially auctioned in Freetown, after it said that the figure was too low.
The "peace diamond", said to be the 14th largest recorded diamond in the world, was handed to the Sierra Leone government in March after it was unearthed by a Christian pastor.