The Munich court did not reveal the beneficiary but said both documents named the same recipient or recipients of the spectacular estate of Cornelius Gurlitt, who died last week aged 81.
The art treasure of Gurlitt, the son of a Nazi-era art dealer, came to light last year, with many works believed to have been stolen or extorted from Jewish collectors, sparking claims by some of their descendants.
A day after Gurlitt's May 6th death, Bern's Museum of Fine Arts said it had been astonished to learn it was the recipient of Gurlitt's collection, an offer it said it was assessing.
With the grant, the museum would become the owner of 1,280 artworks, including long-lost masterpieces by Picasso, Matisse and Chagall, that Gurlitt had hidden in his flat in the southern German city of Munich for decades.
But it appears the museum may have to wait several months to find out whether it will go unchallenged.
On Tuesday a probate court in Munich said it received two separate wills, dated January 9th and February 21st, from a notary from neighbouring Baden-Wuerttemberg state.
More than 200 other paintings, sketches and sculptures were discovered in early February in a separate home of Gurlitt's in Salzburg, Austria including works by Monet, Manet, Cézanne and Gauguin.
The court did not release the names of the beneficiaries, but court president Gerhard Zierl told media that "the wills complement each other", or in other words are not contradictory.
"The heir or heirs are the universal successor," he added, according to national news agency DPA, without confirming the Bern museum.
"They inherit everything," he said.
"I will not say anything about the content."
The court said it would now write to the named beneficiary or beneficiaries, stating that those within Germany would have six weeks, and those abroad six months, to reply.
It also said it would check whether, aside from the named heirs, others may qualify as legal heirs.
For this it would check the records of the deceased parents and siblings of Gurlitt, who was unmarried and childless.
This week, lawyers for a grand nephew of Gurlitt living in Spain said their client may challenge any decision to make the Kunstmuseum Bern the sole beneficiary, DPA reported.
During the Nazi era, Gurlitt's father Hildebrand was tasked with selling works stolen or bought under duress from Jewish families, and avant-garde art seized from German museums that the Hitler regime deemed "degenerate".
Cornelius Gurlitt's vast art hoard — believed to be worth hundreds of millions of dollars — was seized in February 2012 when it was discovered by chance amid a small-scale tax evasion probe.