Swift is believed to be just sixteen and a student at Dublin College painting, which is estimated at £30,000-50,000.
The painting, attributed to Irish artist Thomas Pooley (1646-1723), will be sold live online from Edinburgh by auctioneers Lyon & Turnbull on Wednesday May 18.
Few images exist of the famous Anglo-Irish author (1667-1745), whose works include An Argument Against Abolishing Christianity (1708) and A Modest Proposal (1729).
It is believed to have been painted around 1682, it is being auctioned for the first time in 200 years.
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Nick Curnow, head of fine art at Lyon & Turnbull, said: “This is a remarkable painting of a literary giant of whom few likenesses exist.
“Swift is a very confident role model for a young man and the work has a presence and immediacy that so many 18th century portraits lack.”
The work was acquired by Thomas Percy, Bishop of Dromore, County Down, in 1801, who recorded it as “a small portrait of Dean Swift”.
First exhibited in South Kensington in 1867, it then drifted in and out of public view for the next hundred years.
In 1898 Sir Leslie Stephen, writing in the Dictionary of National Biography, stated that “the present location of this portrait is unknown”.
It reappeared around 1967 in the collection of a descendant of Thomas Percy and around this time it came to the attention of Swift scholars and was attributed to Pooley.
The artist painted many high society figures in Ireland during the second half of the 17th century and early 18th century, contributing to the theory that Swift was the illegitimate son of his benefactor, Sir John Temple (1600 -1677).
Dominic Somerville-Brown, Rare Book Specialist at Lyon & Turnbull, said: “Swift has an enduring hold on readers’ imaginations and an indisputable place in the literary canon.
“However, his legacy does not come with a wealth of images, especially given the era in which he lived.
“So this auctioned portrait is very exciting and I will be thrilled when the auction starts.”