The 130mph Type 57S Atalante is only one of 17 ever made, and could be worth up to £6 million at auction.
That would make it the most expensive car ever to go under the hammer.
Dr Harold Carr died in June 2007 aged 89, a childless bachelor.
He left the lock-up in Newcastle to his nephews and nieces, without telling them of its invaluable contents.
Alongside the Bugatti they also found an E Type Jaguar and an Aston Martin.
They have decided to put the Bugatti, which has not been driven since 1960, up for auction.
It will be the star of Bonhams' Retromobile car sale in Paris on February 7.
Dr Carr's nephew, an engineer from Gosforth, Newcastle, said: "We just cannot believe it was there. No-one had any idea what kind of cars he had parked in there. We knew he had some cars, but we had no idea what they were.
"It was a bit of local folklore that he had a Bugatti, but no-one knew for sure, and certainly no-one knew how much it was worth."
Describing his uncle as "a very eccentric old gent", he said: "It's a wonderful thing to leave."
James Knight, International Head of Bonhams' motoring department said: "I have known of this Bugatti for a number of years and, like a select group of others, hadn't dared divulge its whereabouts to anyone.
"It is absolutely one of the last great barn discoveries, and we at Bonhams are honoured to have been selected to handle its sale."
