A favourite of Hitler, Heesters was born in the Netherlands in 1903 and made his name performing in Nazi Germany.
He died in a clinic in the town of Starnberg in Bavaria where he lived, said his agency Ross.
Heesters played in numerous films and theatre plays, including performing the main role in the Merry Widow, an operetta by Franza Lehar, some 1,600 times.
Heesters' popularity with the Nazis haunted him throughout his life, with protests accompanying his 2008 concert in the Netherlands, his first in decades in his home country.
During his previous concert in the Netherlands in 1963 the audience chased him off by giving him a Hitlerian salute when he appeared on stage.
Heesters had recently been ailing, being cared for in a hospital intensive care unit since December 17.
His death prompted condolences, including one from Bavarian state premier Horst Seehofer who said “elegance and lightness were his trademark.”