A parliamentary committee of lawyers chose the 46-year-old law professor to replace 66-year-old Papier in the leadership change for the Bundesverfassungsgericht, which is located in Karlsruhe.
Voßkuhle, who specialises in administrative and environmental law, will be Germany's youngest-ever high court leader. His deputy will now be 59-year-old Tübingen constitutional judge Ferdinand Kirchhof.
The leader of the constitutional court is elected via parliamentary committee every 12 years.
Voßkuhle, who claims no party affiliation, has had a successful career, becoming Germany's youngest university dean at the University of Freiburg in 2008. Shortly thereafter he was elected as a judge in the high court.