The Foundation for Prussian Cultural Heritage in Germany decided yesterday afternoon to give the painting back to Gerta Silberberg, 85.
In a statement released through her lawyers, Mrs Silberberg, from Leicester, said: "I am very pleased at the outcome and decision of the foundation."
A spokesman said later that she had not yet decided what to do with the painting, which ishanging in the National Gallery in Berlin.
The painting, L'Olivette, belonged to Mrs Silberberg's father-in-law Max. He was ordered to sell his entire collection, which included 143 other works of art by Cezanne, Manet, Renoir and Degas, at a series of forced auctions between 1933 and 1938.
Mrs Silberberg is the first British relative of a Holocaust victim to reclaim work which was sold at these auctions, where property was simply catalogued as "non-Aryan".
A spokeswoman for the Holocaust Educational Trust yesterday welcomed the decision to return the painting.
"It is wonderful that Mrs Silberberg should win her case without being dragged through the courts - she has waited too long already. Museums and galleries around the world must follow this example."
The decision to return the painting to its owner is likely to pave the way for hundreds of other restitutions involving art worth millions of pounds.
The Board of the Foundation for Prussian Cultural Collections voted to give its newly appointed president the power to negotiate returns directly with pre-war owners or their heirs. This is to avoid lengthy court cases and to get around deadlines for making such claims, which have long since passed.
"The expiration of legally set deadlines can't be a reason that injustices are not set right," the president, Klaus-Dieter Lehmann, said.The board's action cleared the way for him to settle Mrs Silberberg's claim.
Museum officials say her claim was clear cut and the painting could be returned to her "within weeks", unless she decides to sell it. Mrs Silberberg has said she has no wish to keep it herself because of the bad memories it brings back.Reuse content