The collection of some 4,300 posters, valued at around €4.4 million ($5.7 million), was taken by the Nazi propaganda ministry from Jewish dentist Hans Sachs, the top poster collector in Germany from the early 20th century.
Later that year, Sachs was sent to a concentration camp but released a few
weeks later, and fled with his family first to London, then to New York. He died in 1974.
In 1961, he received a sum of 225,000 Deutschmarks - more than half a million euros in today's money - in compensation from West Germany. The collection survived the war and languished in the cellar of the German Historical Museum, at the time behind the Iron Curtain in communist East Berlin.
The Federal Court of Justice, based in the western city of Karlsruhe, ruled that the Sachs family "was the owner of the poster collection and can demand it back" from the museum, ending a tug-of-war that had lasted for years.
Not to return the art "would perpetuate Nazi injustice," the court said in a written statement.
The museum said it would accept the judgement and would "shortly" begin talks with the family to decide how to proceed.
Matthias Druba, a lawyer representing the Sachs family, said his client hoped to find another museum in Germany that would display the posters as works of art, not as historical artifacts.
"Ideally this would be in Berlin, because the Sachs family originally came from Berlin," Druba told AFP, adding that they had held back from the search for a new home until the ruling had been handed down.
Hans Sachs's son Peter, who had brought the claim against the museum, is a retired airline pilot and as such "doesn't have the means simply to build a museum," Druba said.
"In any case, this was never about the money, but about restoring the family's history," he said.