Cornelius Gurlitt died "in his apartment in Schwabing, in the presence of a doctor," his spokesman Stephan Holzinger said in a statement, referring to an upscale district of Munich.
Holzinger said Gurlitt had recently undergone serious heart surgery and after spending a week in hospital, asked to return to his home where he had lived among long-lost masterpieces by Picasso, Matisse and Chagall until the collection came to the attention of the authorities two years ago.
Gurlitt had last month struck an accord with the German government to help track down the rightful owners of pieces in his trove of 1,280 artworks, including Jews whose property was stolen or extorted under the Third Reich.
The works, whose value has been estimated at hundreds of millions of dollars, were seized in February 2012 when they were discovered by chance in the course of a small-scale tax evasion investigation.
More than 200 paintings, sketches and sculptures discovered in a separate home of Gurlitt's in Salzburg, Austria including works by Monet, Manet, Cezanne and Gauguin are not covered by the German agreement and it was not immediately clear who would now claim them.
Gurlitt's father Hildebrand acquired most of the paintings in the 1930s and 1940s, when he worked as an art dealer tasked by the Nazis with selling works taken from Jewish families and avant-garde art seized from German museums that the Hitler regime deemed "degenerate".
An eccentric villain
The case only came to public attention when Focus news weekly published an article last year, sparking fierce international criticism that German authorities kept the case under wraps for so long.
Under the April accord, a government-appointed international task force of art experts will have one year to investigate the provenance of all the works in Gurlitt's Munich collection.
Artworks subject to ownership claims after that deadline will be held by a trust until the cases are resolved.
Holzinger said it was unclear whether Gurlitt had left a valid will but a spokeswoman for the Bavarian justice ministry told AFP the April agreement would also apply to any heirs.
"The research on the paintings will go forward without question," the state's justice minister, Winfried Bausback, added in a statement.
A lawyer representing descendants of prominent Paris art collector Paul Rosenberg who have staked a claim to a Matisse portrait in Gurlitt's collection told AFP there were now a number of unresolved issues.
"We obviously will now have to wait for the estate process in Germany to unfold," the attorney, Christopher Marinello, said.
Gurlitt's public image evolved dramatically in the months since his case came to light.
He was initially cast in the German media as an eccentric villain, and told Der Spiegel magazine in a notorious interview last November that he would never give up his collection without a fight. "I will not give anything back voluntarily," he said. "No, no, no."
Gurlitt never married or had children, declaring his art collection to be "the love of his life".
But with the help of a revolving cast of lawyers and advisors, Gurlitt eventually softened his stance and began cooperating with the German government to reach an agreement that was also welcomed by Jewish groups.
German Culture Minister Monika Grütters praised Gurlitt's eventual decision to own up to the historical burden of his spectacular hoard.
"It will remain a credit to Cornelius Gurlitt that he, as a private individual, set an example in the search for fair and just solutions with his commitment to moral responsibility," she said. "He rightly received recognition and respect for this step."
Gurlitt may have another important legacy on the German lawbooks. In the wake of his case, deputies initiated a measure to ditch a 30-year statute of limitations that has provided cover for people in possession of contested artworks.
Gurlitt's father had played a key role in the Nazis' systematic looting of major art collections to raise hard currency and to handpick works for a "Führer Museum" for Adolf Hitler in the Austrian city of Linz that was never built.