A Nazi-looted Matisse painting from the trove of controversial art collector Cornelius Gurlitt was returned Friday to the descendants of its rightful owner.

The oil painting - Woman Sitting in an Armchair by Henri Matisse - was looted from Jewish art collector Paul Rosenberg by the Nazis.

Its whereabouts were unknown for decades until it was discovered in 2012 alongside a trove of 1,280 artworks worth more than a billion dollars in the Munich apartment of the octogenarian recluse.

The painting was formally handed over to Christopher Marinello, a representative of the Rosenberg family, after the move was approved by a court in Munich earlier in the week.

"The descendants of Paul Rosenberg are pleased to confirm the restitution of Matisse's Sitting Woman, which was found in the home of Cornelius Gurlitt in 2012," the Rosenberg family said in a statement.

Experts are in the process of determining which artworks in the trove - which includes works by Gauguin, Dix and Renoir - were looted from Jewish owners. Two Riders on the Beach by Max Liebermann has already been approved for restitution.

Before his death, Gurlitt bequeathed the collection to the Kunstmuseum in Bern, Switzerland.