Green attended Dunbar High School where he practiced football, basketball and baseball. He was an option quarterback that also played defense.

He accepted a football scholarship from Ohio State University to play under head coach Woody Hayes.^[2] As a sophomore, he was named the starter at quarterback over Greg Hare. He was named Big Ten Conference MVP for the 1975 season, when his teammate Archie Griffin became the first two-time Heisman Trophy winner.

Green compiled a 31–2–1 record in the regular season, played in four Rose Bowls, three as the starting quarterback, won the 1974 Rose Bowl against USC, won three Big Ten championships, and led the 1973 team to an undefeated season. In recognition of his Rose Bowl accomplishments, Green was honored with induction into the Rose Bowl Hall of Fame in 2019.^[3]

Although his teams were based on run-oriented offenses, he still held the record of most career passing yards in school history for many years. He finished with 138-of-251 (55.0 percent) attempts for 2,255 yards and 17 touchdowns, while having 409 carries for 2,014 yards (4.9 YPC) and 28 touchdowns.

In 1998, he was inducted into the Ohio State Athletics Hall of Fame.