The goatskin-bound book which was published in 1623 was found at Mount Stuart House on the Isle of Bute and will now go on public display at the stately home for the first time.
Academics who authenticated the book called it a rare and significant find.
"Like hell they have," was professor of Shakespeare studies at Oxford University Emma Smith's first reaction on being told about the discovery.
The discovery comes ahead of the 400th death anniversary of the playwright on April 23.
Adam Ellis-Jones, director of the Mount Stuart House Trust, said the identification of the original First Folio was "genuinely astonishing".
About 230 copies of the First Folio are known to exist. A copy owned by Oxford University sold for 3.5 million pounds in 2003.
The First Folio, printed seven years after Shakespeare's death, brought together 36 plays - 18 of which would otherwise not have been recorded.
The new discovery comes two years after the last copy was found. There is uncertainty about where this copy had been for four centuries since being printed.
Alice Martin, Mount Stuart's head of historic collections, believes it was bought by the third Marquess of Bute, an antiquarian and collector, who died in 1900.
The story of the First Folio usually focuses on the literary genius of Shakespeare, but the survival of his plays depended on the practical skills of the people who produced this book, Smith said.
"I'm sure there are a few more out there. I don't think they're in people's lofts, even though it would be lovely and romantic. I think they're in libraries which have been neglected or forgotten, I suspect more will be in mainland Europe," she added.
Shakespear's body of work consists of 37 plays, 154 sonnets and two long narrative poems.
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