Greene played football as a walk-on at Auburn University, and in 1984 won the Zeke Smith Award as Defensive Player of the Year. He had 69 career tackles as a Defensive End and 11 sacks his senior year. He was selected by the Birmingham Stallions in the 1985 USFL Territorial Draft and later selected by the Los Angeles Rams of the National Football League in the fifth round (113th overall) of the NFL Draft the same year. He played for the Rams for eight seasons, and made the Pro Bowl in 1989 with the team. He later went to the Pittsburgh Steelers, where he made two more appearances in the Pro Bowl and played in Super Bowl XXX, a loss to the Dallas Cowboys. He signed with the Carolina Panthers following their 1995 inaugural season and helped them reach the NFC Championship Game where the team lost to the eventual Super Bowl XXXI champion Green Bay Packers. In 1996 he was named the NFC Linebacker of the Year and received the George Halas Defensive Player of the Year Award. He set an NFL record with 5 consecutive multi-sack games. After one season with the Panthers, he played one season for the San Francisco 49ers before returning to the Panthers for his final two years. He retired in 1999 as a five-time Pro Bowler and the NFL's third all-time sack leader with 160, behind only Bruce Smith and Reggie White. He is one of only 3 players to lead the NFL in sacks in multiple seasons ('94 with the Steelers and '96 with the Panthers). He also ranked third all time in fumble recoveries with 26, which he returned for 136 yards and 2 touchdowns. He also recorded 5 interceptions, returning them for 53 yards and a touchdown.