Experts believe the car could fetch as much as £6 million (A$12.51 million) when it is auctioned at the Retromobile car show and sale being organised by Bonhams in Paris on February 7.
The 130mp/h Type 57S Atalante is only one of 17 ever made and will be the most expensive car to ever go under the hammer at Bonhams.
Former owner, Dr Harold Carr, died in June 2007, aged 89, as a reclusive childless bachelor. He left a garage in Newcastle to his nephews and nieces, without telling them of its valuable contents.
Alongside the Bugatti they also found an E Type Jaguar and a rare Aston Martin. They have decided to put the Bugatti, which has not been driven since 1960, up for auction.
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. The Atalante is incredibly original and, although she requires restoration, it is 'restoration' in the true sense of the word. From my perspective, save for some of the interior, all original parts can be restored or conserved in order to maintain originality."
The Bugatti 57S was originally owned by British aristocrat and racing enthusiast Earl Howe, who was the first president of the British Racing Drivers' Club. He took delivery of the sporty two-seater Atalante in 1937 and kept the car for eight years.
After it changed hands several times, Mr Carr bought it in 1955 and drove it for a few years before parking it in the garage in the early 1960s, where it remained until his death.