A spokeswoman for the ensemble, Claudia Kapsamer, said that the oil painting by Paul Signa will be handed over to Marcel Koch's relatives “before Christmas”.
A Nazi police official gave the orchestra Signa's painting titled Port-en-Bessin in 1940 for its performances in occupied France.
The painting's estimated value is around €470,000 - or $500,000. Marcel Koch died in 1999, childless. His five heirs have said they will take the painting to Paris to be auctioned.
The orchestra purged Jewish members and closely cooperated with Nazi propaganda minister Joseph Goebbels and other associates of Hitler after Germany's 1938 annexation of Austria.
But in recent years it has made efforts to research its Nazi past and to make amends.