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Hoppe was born as son of a master baker in Ellrich, Thuringia, Germany. After his apprenticeship as a baker, he worked from 1945 to 1948 as a coachman. He then began training as an actor in Erfurt and worked in the circus Aeros. He later performed at Thalia Theater in Halle (Saale) and at the Young World Theatre in Leipzig. He acted at the Staatsschauspiel Dresden, the Deutsches Theater in Berlin, and the Salzburg Festival. He was internationally active in Switzerland, Italy, Poland and China.
In the East German DEFA movies, Hoppe often played villains, frequently in different Osterns. One of his most notable roles was that of the Tábornagy (Hermann Göring) in Mephisto, which was awarded the 1981 Academy Award for Best Foreign Language Film.
- 2010: Hoppe spricht Schöne Frühlingslieder
- 1971: National Prize of East Germany 1. class for art and literature
- 1981: Critics Award of the Hungarian Journalist. Association for his role in Mephisto
- 1995: Lessing Award of the Free State of Saxony
- 1998: Grimme-Preis for his role in the TV miniseries Sardsch
- 2005: Goldene Henne for his lifetime achievement
- 2007: Art Award, City of Dresden
- 2010: Order of Merit of the Federal Republic of Germany, 1st Class