Big John - named after the owner of the land where the dinosaur's bones were found - roamed modern-day South Dakota more than 66 million years ago.
The first piece of bone from the supersized skeleton - the skull alone is 2.62 meters long and 2 meters wide - was found in 2014.
By 2015, paleontologists had unearthed 60% of the skeleton, a rare feat, made of over 200 pieces which were painstakingly put together in Italy, to prepare for the Paris auction.
The skull showed a traumatic lesion, which researchers said was likely the work of another triceratops striking it from behind.
The name triceratops means "three-horned face."
The hammer price at the Drouot auction house, before commission and other costs, was 5.5 million euros.
Drouot had estimated the skeleton would fetch between 1.2-1.5 million euros. It sold to an unidentified private U.S. buyer.
Auction house Christie's sold a Tyrannosaurus rex skeleton for $31.8 million in New York last year.