The portrait of Elizabeth Carter, painted between 1735 and 1741 by John Fayram, was found by curators in a private collection.
Carter was part of the Bluestocking group of intellectuals who promoted the advancement of women.
The painting, which will go on display from 13 March, depicts Carter as Minerva, goddess of wisdom and warfare.
It will be part of the National Portrait Gallery's exhibition, Brilliant Women: 18th Century Bluestockings, which will run until 15 June.
'This portrait was part of a campaign to present Carter as an intellectual prodigy, a female celebrity and a virtuous role model for women who might wish to pursue an education,' said the exhibition's co-curator, Dr Lucy Peltz.
The gallery's curators knew of the portrait's existence from a poem published in 1741 and a photograph sent to the gallery in the 1940s.
But the painting, part of a private collection, has never been on public display and was unearthed while curators researched the exhibition.
Carter was well known to her contemporaries for her successful translation of the ancient Greek philosopher Epictetus.
Writer Samuel Johnson once said that his 'old friend, Mrs Carter could make a pudding as well as translate Epictetus... and work a handkerchief as well as compose a poem'.
Text and image by BBC News, UK