Voigts was a native of Evanston, Illinois, where Northwestern's main campus is located. He attended Northwestern and played on the school's football team between 1936 and 1938. In his sophomore year, the Wildcats won the Big Ten Conference, and Voigts was named an All-American tackle. After college, Voigts served as an assistant football coach and head basketball coach at Illinois Wesleyan University before moving briefly to Yale University, where he was a football line coach. He entered the U.S. Navy during World War II in 1942 and was stationed outside of Chicago where he met Paul Brown, the head coach of the base's football team. When Brown became head coach of the Cleveland Browns after the war, he hired Voigts as a tackle coach. After a year with the Browns, Voigts became head coach at Northwestern.