Born in Vienna, Cornelius Obonya comes from a dynasty of actors: his parents are Elisabeth Orth and Hanns Obonya (died 1978), his maternal grandparents were Paula Wessely and Attila Hörbiger.
At the age of 17, he went to the Max Reinhardt Seminar to study acting, but left after a year to study with the cabaret artist Gerhard Bronner. Bronner was one of the most important encounters in his career, as was Emmy Werner, the former director of the Volkstheater Vienna, and Andrea Breth, with whom he worked for many years at the Schaubühne Berlin and the Burgtheater Vienna. Cornelius Obonya is married to director Carolin Pienkos and father of their son Attila.
For his first role at the Volkstheater, Eugene in Brighton Beach Memoirs by Neil Simon, Cornelius Obonya was awarded the Karl Skraup Prize for young talent in 1989; the following year he received the O.E. Hasse Prize. He already worked with Andrea Breth during his engagement at Berlin's Schaubühne am Lehniner Platz (1992-1999), followed by Edward Bond's The Sea (Hollarcut), Lessing's Emilia Galotti (Pirro), Schiller's Don Carlos (Domingo), Chekhov's The Cherry Orchard (Trofimov), Tennessee Williams' The Cat on the Hot Tin Roof (Gooper) and Lessing's Minna von Barnhelm (Paul Werner) at the Burgtheater from 2000. At the Burgtheater, Cornelius Obonya has also played also under the direction of Peter Zadek, Sven-Eric Bechtolf, Karin Beier, Carolin Pienkos, Anselm Weber, Stefan Bachmann and Falk Richter; he was Caligula in Albert Camus' play of the same name (director: Jan Lauwers), Herr von Rappelkopf in Ferdinand Raimund's Der Alpenkönig und der Menschenfeind (director: Michael Schachermaier) and most recently Caius Martius Coriolanus in Shakespeare's Coriolan (director: Carolin Pienkos).
In 2008/2009 he played and sang in Mel Brook's Broadway musical The Producers at the Ronacher in Vienna and at the Admiralspalast in Berlin. In the 2009/10 season, he made a guest appearance at the Theater in der Josefstadt as the teacher in Jugend ohne Gott by Christopher Hampton based on Ödön von Horváth (director: Torsten Fischer). He celebrated great success in 2010/11 with his solo evening Cordoba - Das Rückspiel by Florian Scheuba and Rubert Hennig at the Rabenhof Theater in Vienna. For this he received the "Salzburger Stier 2010" and a nomination for the "Special Prize of the Nestroy Award 2010". In the same year, he was named "Actor of the Year" by the Austrian Broadcasting Corporation (Ö1). In 2012 and 2013, he began his collaboration with the Stadttheater Walfischgasse, where he appeared as Andrew Wyke in Revanche by Anthony Shaffer and as Leroy Brooks in the world premiere of C(r)sah, written by Rupert Henning and also directed by Carolin Pienkos.
Cornelius Obonya made his debut at the Salzburg Festival in 2002 as Paul Kreindl in Andrea Breth's production of Schnitzler's Das weite Land. In 2012, he was Monsieur Jourdain in the opera Ariadne auf Naxos by Richard Strauss/Hugo von Hofmannsthal, based on Molière's Bürger als Edelmann in the adaptation by Hugo von Hofmannsthal. Cornelius Obonya was celebrated as Jedermann in the Salzburg Festival summers from 2013 to 2016.
On the big screen, Obonya has appeared in Spain (directed by Anja Salomonowitz), in Peter Patzak's Kottan ermittelt - rien ne va plus, in Egon Schiele (directed by Dieter Berner) and as Konrad in Die Trapp Familie - ein Leben für die Musik (directed by Ben Verbong). He has also appeared in numerous TV productions, including the crime series Tatort and CopStories, Nachtschicht by Lars Becker and TV films such as Polt and Die Hebamme. Since 2018, he has appeared in the series Meiberger - Im Kopf des Täters and in the Altaussee crime series on ServusTV. He also shot for Costa-Gavras in his film Adults in the Room in 2019.