Speedie was hired in 1960 as an end coach for the Houston Oilers in the American Football League (AFL). The Oilers won the AFL championship that year, but Speedie left in 1961 after the head coach, former teammate Lou Rymkus, was fired. He then took a job as an assistant for the AFL's Denver Broncos and was promoted to head coach in 1964. His two-year run with the team was unsuccessful, however. After his resignation in 1966, Speedie became a scout for the Broncos, a job he kept until his retirement in 1982. On January 15, 2020, Speedie was announced to have been selected to the Pro Football Hall of Fame class of 2020.