Dodd was born in Galax, Virginia. He moved to Kingsport, Tennessee and played several sports at Dobyns-Bennett High School. After high school, he played as a quarterback at the University of Tennessee. From 1931–1945, he worked as an assistant coach for William Alexander at Georgia Tech. Alexander hired Dodd while he was still a student at Tennessee. Dodd replaced Alexander in 1945 and became the third head coach at Georgia Tech. He retired from coaching after the 1966–67 season, with 165 wins, 64 losses, and 8 ties in his career. He also worked as athletic director for Georgia Tech from 1950 until 1976. Dodd died in June 1988 at the age of 79 in Atlanta, Georgia.