Conrad graduated from Augustana College, Rock Island, Illinois in 1915 and earned his M.A. at the University of Pennsylvania in 1916. He returned to Rock Island to complete the B. Div. degree at the Augustana Theological Seminary. He was ordained into the ministry of the Augustana Lutheran Synod on June 12, 1921 in Chicago. He pursued advanced study at Sweden's Uppsala University, serving as personal secretary to Swedish Archbishop Nathan Söderblom during the Stockholm Conference on Life and Work in 1925. He earned his Ph.D. from the University of Chicago in 1928.

He went on to become president of Augustana College in 1935. He used his considerable influence and power within the Augustana Synod to help unite those Swedish-background churches into the United Lutheran Church in America (1962-1987), a precursor of the current Evangelical Lutheran Church in America.