Gurlitt hoarded the works for decades in his Munich flat and house in Salzburg, Austria, after inheriting them from his father Hildebrand, who sold works taken or bought under duress from Jewish families and 'degenerate' avant-garde art stolen from museums.
Museum president Christoph Schäublin told a press conference in Berlin that the potentially-stolen works would remain in Germany while investigations continued.
A police taskforce founded after Gurlitt's death will continue to investigate their ownership under an agreement between the museum and German authorities.
Culture Minister Monika Grütters called the agreement reached after six months of negotations "a milestone in coming to terms with our history," and that the German government would return looted works to Jewish descendants "as soon as possible, with no ifs, ands or buts."
But the government was "at the beginning, not the end, of a long road," she said.
The German government will pay the costs of restoring stolen artworks to their rightful owners under the agreement, which will be signed by Grütters and Bavarian justice minister Winfried Bausback on Monday.
The transfer of the works to the Swiss museum has been controversial in Germany, with Ronald Lauder, head of the World Jewish Congress, telling Spiegel in November that it would "open a Pandora's Box and cause an avalanche of lawsuits."
Gurlitt's collection of 1,280 artworks was discovered in 2012 when his apartment was searched after he fell under suspicion for tax evasion.
But details only became known to the public after the find, kept secret by the authorities, was leaked to Focus magazine.
He agreed to return unconditionally any art found to have been stolen shortly before his death aged 81 in May this year, as well as making the will leaving the remainder of the collection to the museum.