Stob studied at both Calvin College and Calvin Theological Seminary before receiving his Ph.D. from the University of Gottingen in 1938. He served the College as Associate Professor of Philosophy from 1939 to 1943. In 1943 he entered the armed forces as a Lieutenant in the United States Navy.
Upon his discharge in 1946, he taught at the College as Professor of Philosophy until 1952. In 1952, he was appointed Professor of Ethics and Apologetics at Calvin Theological Seminary. Stob retired from the faculty in 1975 and received the Calvin College Distinguished Alumni Award in 1976.
In 1975, an endowment was established at Calvin in honor of Dr. Stob, the proceeds of which have underwritten the Stob Lectureship held annually under the sponsorship of both the Seminary and the College.
The subject matter of the Stob Lectures relates to the fields of apologetics, ethics, and philosophical theology. Over the years, scholars such as Lewis Smedes, Richard Mouw, Miroslav Volf, Mary Steward Van Leeuwen, and Sarah Coakley have presented the lectures.