Many of the works are expected to remain in Germany until their rightful owners can be identified.
Cornelius Gurlitt, the son of Adolf Hitler’s art dealer, amassed a priceless collection of works, including pieces by Picasso and Monet.
He died in May aged 81 with the Bern museum named his “sole heir”.
The Bavarian authorities seized some 1,280 artworks from his Munich flat as part of a tax evasion probe in February 2012.
The find, which was not made public until November last year, has triggered legal disputes surrounding works taken illegally by the Nazis.
The Bern museum’s president, Christoph Schaeublin, told a news conference in Berlin on November 24 that the museum would accept the bequest.
But “no work suspected of being looted” would enter the museum, he said.
The museum pledged to work with German authorities to ensure that “all looted art in the collection is returned” to its rightful owners.
“The foundation council’s decision was anything but easy and there certainly weren’t emotions of triumph,” said Christoph Schaeublin.
“These would be entirely inappropriate considering the historic burden weighing heavily on this art collection.”
Cornelius Gurlitt’s father, Hildebrand Gurlitt, was ordered to deal in works that had been seized from Jews, or which the Nazis had considered “degenerate” and removed from German museums.
Among the collection were works by Pierre-Auguste Renoir, Pablo Picasso, Marc Chagall, Emil Nolde and Max Liebermann.
A German task force is investigating the art amid claims from descendants of the original owners, including the family of art dealer Paul Rosenberg.
Cornelius Gurlitt initially refused to give up the paintings but then changed his position, agreeing to co-operate with the German authorities on establishing the paintings’ provenance, and then return them if they were shown to be stolen.
Cornelius Gurlitt’s cousin, 86-year-old Uta Werner, said on November 21 she was contesting his fitness of mind when he wrote the will naming the Bern museum as his sole heir.
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