The fossilised remains of 'Big John' had an estimate of €1.2m-1.5m at the October 21 sale at the Drouot auction centre. Including premium, the buyer will pay €6.4m.
The skeleton was named Big John after the owner of the land in the USA where more than 200 of the dinosaur's bones were found.
Palaeontologists unearthed the first piece of bone in 2014 and eventually found 60% of the skeleton during 2015, including a 75% complete skull measuring 8ft 5in (2.6m) long and 6ft 6in (2m) wide.
The bones, still enveloped in rock, were taken to Trieste in Italy last year to be cleaned and put together.
Big John roamed the lands of modern-day South Dakota more than 66 million years ago. The area, referred to as Laramidia, was an island continent stretching from present-day Alaska to Mexico. The dinosaur died in an ancient flood plain - the current Hell Creek geological formation allowing the conservation of the skeleton in mud.
Dinosaur skeletons are popular at auction.
Last year a complete Tyrannosaurus rex skeleton was sold at auction at Christie’s New York for a hammer price of $27.5m (£21.3m).
The specimen, known as Stan, is one of the largest, most complete and widely studied T-rex skeletons ever discovered. It is named after the palaeontologist Stan Sacrison who found the skeleton’s partially unearthed hip bones in 1987 in South Dakota.