Green was selected as the seventh overall pick of the first round by the Buccaneers in the 1981 NFL Draft. He was a 1982 All-Pro and 1983 All-Pro and was elected to the Pro Bowl twice in his career, in 1982 and 1983. Later in his career he suffered several injuries, including a car accident in the middle of the 1984 season for a fracture near the eye. He was traded to the Miami Dolphins in the middle of the 1985 season in exchange for their first- and second-round draft choices in the 1986 draft. In the 1985 season he was on to a career-high in sacks and ended the season getting 7.5 while playing all 16 games despite the mid-season trade.