The print, a portrait of the Amsterdam preacher Jan Cornelis Sylvius (1564-1638), was previously noted as a copy of a work by Rembrandt.
Dr Tico Seifert, the gallery's senior curator for Northern European Art, has now established that the etching is the work of the Dutch master.
Dr Seifert's research has also confirmed that this is the only known version of the image to have been printed in red ink.
The Portrait of Jan Cornelis Sylvius, which is estimated to be worth hundreds of thousands of pounds, is now on public display.
Dr Seifert said: "I became suspicious once I found that all the known copies of this print are in reverse - which this one obviously wasn't.
"With mounting excitement I made further comparisons and it became increasingly clear that I was not dealing with the work of a copyist but looking at an etching by Rembrandt himself.
"I then contacted colleagues in Amsterdam to find out about impressions in red ink, which are generally very rare.
"To my great surprise and delight they told me it is a unique print."
The work is held in the The Print Room of the Scottish National Gallery, which houses more than 100 impressions of Rembrandt etchings.
Dr Seifert added: "It is immensely thrilling when we make a discovery of this kind."
Rembrandt (1606-1669) made his Portrait of Jan Cornelis Sylvius in 1633, shortly after moving to Amsterdam from his hometown of Leiden.
The subject of the portrait was a relative of Saskia van Uylenburgh (1612-1642) whom Rembrandt married that year.
Sylvius became the godfather to the couple's first child and baptised their daughter Cornelia in 1638, the year he died.
The Portrait of Jan Cornelis Silvius will be shown alongside an impression of the same image in black ink, which shows further reworking, and which was probably printed later in the 18th century.