Christoph Edel, Mr Gurlitt's lawyer, phoned the museum on May 7, the day after his client died, to tell it that it was "his unrestricted and unfettered sole heir".
It is just the latest twist in the extraordinary tale of a hoard of art worth hundreds of millions of pounds originally stashed by Mr Gurlitt's art dealing father, Hildebrand, who had been ordered to dispose of works deemed degenerate by the Nazis.
Bavarian authorities seized the hoard of more than 1200 works when it came to light in Mr Gurlitt junior's Munich apartment in 2012 - around another 300 were later discovered in a second home - since when it has been at the centre of legal investigations.
In February, a deal was finally struck by which hundreds of works would be returned to Mr Gurlitt while the remainder would continue to be investigated.
The museum published a statement, saying: "The Board of Trustees and Directors of Kunstmuseum Bern are surprised and delighted, but at the same time do not wish to conceal the fact that this magnificent bequest brings with it a considerable burden of responsibility and a wealth of questions of the most difficult and sensitive kind, and questions in particular of a legal and ethical nature. They will not be in a position to issue a more detailed statement before first consulting the relevant files and making contact with the appropriate authorities."