The 1937 painting by Henri Matisse -- "Woman in Blue in Front of a Fireplace" -- worth an estimated $20 million (14.5 million euros), was claimed by the Rosenberg family after it appeared in a temporary exhibition at the Paris Pompidou Centre in 2012.
The piece -- which has been returned by the Henie Onstad art centre near Oslo -- was seized in France by the Nazis in 1941, and was briefly part of the personal collection of Luftwaffe chief Hermann Göring.
It later found its way into the hands of a German art dealer Gustav Rochlitz who owned a gallery in Paris.
In 1950, a wealthy Norwegian shipowner Niels Onstad bought the painting from the Parisian dealer Henri Benezit without knowing how he had acquired it.
The Matisse went on to form one of the centre-pieces of the Henie Onstad art centre, established in the 1960s by Onstad and his wife, the Olympic figure skating champion Sonja Henie.
Although Norway is a signatory to the Washington Conference Principles on Nazi-Confiscated Art it also has a law which grants definitive ownership once a collector has possessed an item for more than a decade.
"Henie Onstad art centre's extensive investigation of the case has led to the decision that the return is justified, and HOK's board has decided to return the painting without further conditions," board chairman Halvor Stenstadvold declared on Friday, announcing the unconditional return of the piece.
Now the "Woman in Blue in Front of a Fireplace" will cross the Atlantic following an agreement between the French and American sides of the Rosenberg family.
"There is no (contentious) issue," Christopher Marinello, the Rosenberg's lawyer who travelled to Norway to collect the painting, told AFP.
The family was continuing to actively search for "hundreds of works" looted by the Nazis during the war, he added.