Experts knew of the portrait’s existence but did not know where to find it. A five-year search eventually ended when an advert was placed in a magazine. It will be seen as part of an exhibition, Gainsborough’s Family Album, at the National Portrait Gallery in London.
The show will focus on works Gainsborough created “for love, rather than money” and track his life from “relative obscurity to being one of the leading lights of the British art world”.
Curator Lucy Peltz said: “One or two pictures eluded us for a long time and this was one.
“Representatives of the owners discovered we were looking for it after we put the notice in.”
The painting, Margaret Gainsborough, The Artist’s Daughter, Playing A Cittern, was still in Gainsborough’s possession when he died and stayed with his descendants until the 1870s.
Co-curator David Solkin said that since the work was not for sale, Gainsborough had no economic imperative to finish it.
The rediscovered work, whose owners want to remain, is the only portrait to combine Gainsborough’s greatest loves – music and his daughters, whose artistic interests he encouraged.