Wess was born in Oberwölz Stadt, a small town in the Austrian state of Styria. He received his Ph.D. in Vienna, where he was a student of Hans Thirring. His Ph.D. examiner was acclaimed quantum mechanics physicist Erwin Schrödinger. After working at CERN in Switzerland and at the Courant Institute of New York University, United States, he became a professor at the University of Karlsruhe. In later life, Wess was professor at the Ludwig Maximilian University of Munich. After his retirement he worked at DESY in Hamburg.