Edwards was drafted in the first round of the 1977 NFL Draft, the third overall selection, by the Cincinnati Bengals. He played for the Bengals for 12 seasons from 1977 until his retirement in 1988. During that time, he recovered 17 fumbles and set a franchise record with 83.5 sacks. However, only 47.5 of those sacks are "official", as the NFL did not consider sacks an official statistic until 1982. His 47.5 official sacks are still a Bengals franchise record to this day.
Edwards was inducted into the University of Miami Sports Hall of Fame in 1989.