He grew up with his mother, actress Hannelore Wüst, and step-father Gerhard Scheumann, a well-known East German documentary film maker.
He studied at the Gerasimov Institute of Cinematography in Moscow, but was pulled from his studies and lost his Communist party membership for his support of dissident Wolf Biermann after Biermann was stripped of his East German citizenship in 1976.
After serving as an assistant director to Thomas Langhoff, Eberhard Fechner and Diethard Klante, Geschonneck released his first feature film Moebius [de] in 1992, followed by a series of episodes of the popular German television crime series Tatort.
In 1995, he directed the TV movie Matulla und Busch, which was the last film his father starred in.
His 2022 TV film Die Wannseekonferenz, about the 1942 Wannsee Conference to plan the Holocaust, received multiple recognitions.