He originally wanted to be a musician, but a production by artistic director Claus Peymann influenced him in the late 1970s to change careers to become an actor.

His first international productions included the historical drama series Napoleon, in which he appeared alongside Gérard Depardieu, John Malkovich, and Isabella Rossellini.

Koch has portrayed other historically significant personalities, including Rudolf Höss in Costa-Gavras' adaptation Amen (Der Stellvertreter).

Koch himself was nominated several times for his work in the film, receiving the Globo d'oro for Best European Actor, The Quadriga, and the Bambi Award.

The shooting of this two-parter based on Nigel Williams’ script and under Mike Barker’s direction took place in Halifax, Canada.

The shooting of the movie Manipulation (adapted from the novel Das Verhör des Harry Wind) took place in 2008, with Koch and Klaus Maria Brandauer playing leading roles.

In 2013, Ridley Scott (director and producer) began working on The Vatican, a pilot episode for a Showtime series about intrigues concerning the Pope and mysteries and secrets within the Catholic Church.

The biographical romantic drama film The Danish Girl by Academy Award winner Tom Hooper (The King's Speech) is about one of the first known recipients of sex reassignment surgery.

Eventually, in 2015, Koch began shooting the fifth season of the Showtime series Homeland about bipolar CIA Officer Carrie Mathison (Claire Danes).

After leaving the CIA, Carrie now works for German billionaire Otto Düring (Koch), a philanthropist who uses the money his family made through affiliation with the Nazis to help struggling people around the world, including in volatile regions of the Middle East.

In 2016, he collaborated again with director Florian Henckel von Donnersmarck for the feature film Never Look Away, produced by Wiedemann & Berg and Walt Disney.

Koch stars alongside Tom Schilling, Paula Beer, Saskia Rosendahl, Oliver Masucci and Ina Weisse.

In the thriller series Your Honor (German title Euer Ehren), a German-Austrian adaptation of the Israeli series Kvodo, which aired in April 2022, Koch embodies a incorruptible judge who violates his moral principles and breaks with law and order driven by the infinite love for his son and the concern for his son's life.

[1] In addition to his acting work, he also does symphonic-scenic readings, including Paradise with violinist Daniel Hope, Dream Story with the Hubert Nuss Jazz Quartet and The Kreutzer Sonata after Leo Tolstoy, which Koch dramaturgically adapted and conceived as a stage play with piano and violin.