Born in Chemnitz as the younger son of Jewish parents,[2] Degen survived the Holocaust in Berlin, while his older brother was sent to Palestine via Denmark and Sweden.

[5] In 1946, Degen appeared on stage for the first time[2] and received his education through a scholarship at the acting school of the Deutsches Theater in East Berlin.

[8][9][10] A reviewer of The Times wrote of Degen's acting in Harry Buckwitz's 1965 Hamlet production at Schauspiel Frankfurt, "Nervously impulsive and sometimes violently emotional".

[11] Degen performed in Munich, Salzburg and Hamburg and worked with directors including Ingmar Bergman, George Tabori[12] Peter Zadek[13][14] and Claude Chabrol.

[3][15] He was Moliere's Dom Juan in Ingmar Bergman's production at the Salzburg Festival[16] and Adam in Kleist's The Broken Jug.

[20][3][21] He played Adolf Hitler in Michael Kehlmann's 1988 film Geheime Reichssache [de] as well as Dr. Martin Sanders in Diese Drombuschs.

[9] In 2006, Jo Baier filmed Degen's memoirs with Aaron Altaras and Nadja Uhl for ARD (Not All Were Murderers [de]).