Yeoman played center for Army from 1946 to 1948 under legendary head coach Earl Blaik. The 1946 team was 9–0–1 with a backfield of two Heisman Trophy winners: Glenn Davis and Doc Blanchard. Yeoman was a team captain in 1948 and chosen as a second team All-American. The Army football teams in which he played compiled a combined 22–2–4 record. Bill Yeoman is still the only underclassman to ever captain an Army team.