Heesters died Dec. 24 at a hospital in Starnberg, Germany, where he had been in critical condition for several days, said his agent, Juergen Ross.
He gained fame by appearing in films such as "Die Leuchter des Kaisers" (The Emperor's Candlesticks) and "Das Hofkonzert" (The Court Concert).
Despite his popularity in the Third Reich, Heesters was never accused of being a propagandist or anything other than an artist willing to perform for the Nazis, and the Allies allowed him to continue his career after the war, when he took Austrian citizenship.
In Heesters' native Netherlands — which was occupied by Germany for most of the war — some viewed him as irredeemable given his appearances under the Nazi regime.
In early 2008, he braved protests to perform in the Netherlands for the first time in 44 years at a theater in Amersfoort, his birthplace.
He had been booed off stage in 1964 in Amsterdam when he tried to portray Nazi-hating Captain Von Trapp in "The Sound of Music."
Heesters said it gave him a "heavy heart" to know he was "not wanted in my homeland."
"What did I do wrong? Sure, I acted in films in the Third Reich, entertainment films, which distracted countless people ... during war," he later wrote.
"Sure, I wanted to make my career and I remember well at the time how many people in the Netherlands were proud that I made a career in the huge neighboring country," he added. "But apart from my career — and the fact that, through no fault of my own, Adolf Hitler was one of the fans of my art — what have I done?"
Critics focused on a visit Heesters made to the Dachau concentration camp in 1941.
In late 2008, Heesters lost a court attempt to force a German author to retract allegations that he sang for SS troops there.
Heesters maintained that the Nazis had ordered him to Dachau in an attempt to deceive the public about what was really going on there, but said the performance "never happened."
But Berlin author Volker Kuehn cited an interview with former Dachau inmate Viktor Matejka in which the prisoner recalled, "I pulled the curtain for him, I was there, I saw him singing."
Around the time of the court case, Heesters was shown on Dutch television calling Hitler "a good guy." Heesters' wife, Simone Rethel, immediately intervened to say that Hitler was the worst criminal in the world.
"I know, doll," Heesters responded. "But he was nice to me."
Rethel protested after the clip aired, telling Dutch papers that he had been tricked into making the remarks, and that parts of the interview in which Heesters condemned the Nazi regime had been cut.
Heesters continued to be a popular performer in Germany well into his old age. He made 1,600 appearances in his best-known role, as Count Danilo in Franz Lehar's operetta "The Merry Widow," and 750 as Honore in the musical "Gigi."
At age 98, he performed in Chekhov's "The Cherry Orchard." As he turned 105, Heesters was appearing in a musical comedy.
"To have nothing to do, to sit there waiting for little aches and pains, is fundamentally wrong," he once wrote. "Life has to be lived."
Heesters was born Dec. 5, 1903, the youngest of four sons of a businessman. His first wife, Dutch actress Louisa Ghijs, died in 1983. The couple had two daughters, Nicole and Wiesje. He married Rethel, a German actress, in 1992.