Mr Andrews said the Bugatti will be the only one of its kind in New Zealand, and will be displayed at his museum.
He owns about 140 classic cars, but said this one was "definitely the most valuable".
The Bugatti Type 57s were designed by its founder Ettore Bugatti's son, Jean, and built between 1934-1940.
Just 710 examples were produced, and a rediscovered Type 57 sold for $5.2 million at a Paris motor show in 2009.
The car Mr Andrews bought had belonged to shipping magnate Roger Baillon, who collected fine vehicles in the 1950s with the intention of starting his own museum, but had to sell off half of them when his business faltered in the 1970s.
The rest of the cars were left parked in various states of exposure.
The collection, called the King Tut of barn finds, included a rare 1961 Ferrari 250 GT SWB California Spyder that once belonged to actor Alain Delon.
Only 37 were built and the Ferrari sold for $21.5 million.
Bugatti Type 57 • Designed by Jean Bugatti, son of founder Ettore. • Produced between 1934-40, only 710 were built. • Grand tour class. • Engine 3257cc DOHC In-line 8. • Engine used gears to transmit power from the crankshaft.