It is expected to make up to $4m (£2.2m) at auction in New York next year, the 400th anniversary of Rembrandt's birth.
As an oil sketch, it is relatively uncommon, compared with the large number of Rembrandt drawings and full paintings to have survived. But, virtually forgotten by scholars, the painting has not been illustrated or exhibited since the 1930s, when doubts arose over its authenticity.
It was dropped from catalogues of his work, and when Mr and Mrs Walsh - Texas oil tycoons - bought it in New York it had been long out of public view.
Three years ago, the Walsh family invited George Wachter, vice-chairman of Sotheby's, to take a look. Examining the work's surface, he noticed areas of superior paintwork contrasting with areas which were less successful. He decided to investigate further, and showed it to one of the world's leading Rembrandt experts, Ernst van de Wetering, head of the Rembrandt Research Project.
George Gordon, a Sotheby's old masters expert, said: "This is not a picture sitting around unloved in an attic. It was a picture they had on their walls. It was quite dirty, not just discoloured varnish but with over-paint. But what struck all of us when we saw it was the extraordinary quality of the bonnet. It was very Rembrandt-esque."
X-ray and pigment analysis was carried out by Martin Bijl, formerly head of paintings conservation at the Rijksmuseum in Amsterdam. Studies of the wood revealed that the oak panel on which it was painted was taken from the same tree as was used for three other panel paintings by Rembrandt or his studio.
Finally, layers of over-paint which had been added in the late 17th century were removed, revealing that the woman's face was, for the most part, in shadow, and that her bonnet was in full light. It suggested that, far from being a formal portrait, the work was a study of an old woman in which Rembrandt experimented with new effects of lighting.
Mr Gordon said there were some clues even before the restoration began, notably that a fur collar she was wearing must have been a later addition. "She's now got this rather beautiful linen collar which is what you would have expected her to have worn with a cap like this," he said.
"Under her chin, you can actually see where the light is reflecting back up into the lower part of her chin. You couldn't have got that from a fur collar. Rembrandt was an absolute master of half-tones, parts that are in shadow, that are receiving back light."
Mr Wachter said the quality of the paint-handling was outstanding, particularly in the bonnet, collar and ear. "But the more you examine it, the panel continues to reveal details that reinforce Rembrandt's superior abilities - his delicate treatment of her hair, the realistic quality of the metal ear iron and the reflection of the collar on her jaw and chin."
In the spring of this year, at the conclusion of the tests and restoration, Professor van de Wetering concluded the work was without question by Rembrandt.
It was probably produced around 1640 and is thought to be a domestic servant in the artist's household - and not the artist's mother, as some have speculated, as the dates do not tally.
The painting is on show at the Rembrandt House museum in Amsterdam until next month and can be seen at Sotheby's offices in New York, London (for a week in December), Boston and Los Angeles prior to sale in New York on 26 January.Reuse content