Il Gran Mogol, which belonged to a quartet of lost concertos, has been authenticated as the work of the 18th Century Italian composer.
Southampton University research fellow Andrew Woolley found the piece among the Marquesses of Lothian’s family papers at the archives in Edinburgh.
It will receive its modern day premiere at Perth Concert Hall in January.
The other pieces of the quartet – La Francia, La Spagna and L’Inghilterro – remain lost.
Il Gran Mogol is almost complete, only missing a part for the second violin.
But Mr Woolley has reconstructed it using the manuscript of another flute concerto by Vivaldi, which is kept in Turin and appears to be a reworking of Il Gran Mogol.
He said: “This piece was previously known only from a mention in the sale catalogue of an 18th Century Dutch bookseller.