Overbeck studied theology and philosophy at University of Münster and at Collegium Germanicum et Hungaricum in Rome.

[4] In 2010 Overbeck was appointed Church assistant to the foundation Centesimus Annus Pro Pontifice (CAPP).

[5] On 24 February 2011, Overbeck was given the additional responsibility of bishop of the Military Ordinariate of Germany;[2] he was installed on 6 May.

[8] In September 2023, Overbeck acknowledged mistakes in handling the sexual allegations against Cardinal Franz Hengsbach, who led the diocese for three decades, finally stepping down in 1991 at the age of 80.

[10] In January 2019, Overbeck said there should be reforms in Roman Catholic sexual ethics and that same-sex marriages should be accepted and not be described as immoral.