Kobus was born in Szczytno, Poland and, as an ethnic German, moved to Germany in 1970. From 1988 until 1991 he attended the school of performing arts Otto-Falckenberg-Schule in Munich, Germany. Afterwards he performed in several theatre plays in Frankfurt, Bochum, Stuttgart, Zürich, Vienna and Cologne. He has starred in TV shows since the early 1990s and as of 2001 began to be recognised by the public for his roles in movies and TV shows, in particular thanks to his role in the German comedy show Alles Atze, in which he plays the police officer 'Viktor Schimanek'. His international breakthrough was his 'SS officer Günther Franken' role in the movie Zwartboek (Black Book) by Dutch director Paul Verhoeven.