The drawing of a bearded man is believed to be one of only two surviving portraits made during the artist’s life time.
Martin Clayton, head of prints and drawings at the Royal Collection, uncovered the image while examining papers stored in Windsor Castle.
He identified it as a study of Leonardo made by an unidentified assistant shortly before the artist’s death, aged 67, in 1519.
The only other contemporary portrait was made at around the same time by Leonardo’s pupil Francesco Melzi, the expert said.
Another drawing in Turin is widely believed to be a “self-portrait” of the Italian master but Mr Clayton and other experts have questioned the claim.
“If you compare this sketch with Francesco Melzi’s portrait of Leonardo, you can see strong indications that this too is a depiction of the artist,” said Mr Clayton.
“The elegant straight nose, the line of the beard rising diagonally up the cheek to the ear, a ringlet falling from the moustache at the corner of the mouth, and the long wavy hair are all exactly as Melzi showed them in his portrait.
“Alongside Melzi’s portrait, this is the only other contemporary likeness of Leonardo.”
Mr Clayton said Leonardo was aged around 65 in the sketch and appeared “a little melancholy and world-weary”.
“He knew that he was dying,” the expert added. ”A paralysis had struck his right arm, he could no longer paint – he could still draw – and he knew that his body was failing.”
He added: “Leonardo was renowned for his well-kept and luxuriant beard, at a time when relatively few men were bearded – though the beard was rapidly coming into fashion at this time.”
The portrait appears on a double-sided sheet of paper bearing Leonardo’s detailed studies of a horse’s leg for an equestrian monument.
Art historian Kenneth Clark suggested that it was ”just conceivable” that the portrait was of da Vinci when he compiled a scholarly catalogue of the drawings in the collection in 1968.
But the Royal Collection Trust said the suggestion went no further and it has only been positively identified during Mr Clayton’s research.
It will be displayed alongside 200 drawings by the artist in an exhibition at the Queen’s Gallery from 24 May.
Other highlights include Leonardo’s studies for The Adoration of the Magi painting and The Last Supper.
In November a selection of 80 drawings will move to the Queen’s Gallery in Edinburgh for the largest exhibition of da Vinci’s works shown in Scotland.
Additional reporting by Press Association
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