Stosch studied Catholic theology from 1991 to 1997 at the University of Bonn and the University of Fribourg in Switzerland. In 2001, he completed his doctorate in dogmatics with Karl-Heinz Menke. In 2005, he completed his habilitation with Jürgen Werbick at the University of Münster for fundamental theology. Since the winter semester 2008/2009 Stosch has been professor for systematic theology and didactics at the University of Paderborn. Stosch played a central role in founding the Centre for Comparative Theology and Cultural Studies at the University of Paderborn, which he has been directing since 2009.
Research stays have taken von Stosch to the Center for the Study of World Religions at the US Harvard Divinity School and the University of Religions and Denominations in Qom, Iran .
In 2009, he was awarded the Research Prize of the University of Paderborn for his project “Islam in Germany – Intercultural and Interreligious Discourse in Literature” (with Prof. Dr. Michael Hofman).