Drafted in the second round of the 1981 NFL Draft (53rd overall) from the University of Pittsburgh, Jackson was a member of the first Bum Phillips draft in New Orleans. He played in all 16 games his rookie season and was named to the NFL All-rookie team. In 1983 he was First-team All-NFC, the first of seven seasons in which he'd receive post-season honors in the NFL, including being six-time Pro Bowl selection (1983, 1984, 1985, 1986, 1992, 1993). Jackson was a four-time First-team All-Pro and a two-time Second-team All-Pro selection. In 1994, Jackson joined the 49ers, where he won his first and only Super Bowl.
Jackson recorded 10 or more sacks in six different seasons and led the NFL in fumble recoveries in 1990 and 1991. He finished his career with 136 (8 unofficial in 1981) sacks and 8 interceptions, which he returned for 68 yards. He also recovered 29 fumbles. At the time of his retirement, his 28 defensive fumble recoveries were the second most in NFL history behind Jim Marshall's 29. He still leads the Saints in career sacks with the team with 123.
In his entire 13 seasons as a Saint, Jackson missed only 2 games, and those 2 games were a result of an automobile accident he suffered in 1989. He played the remainder of the 1989 season with his jaw wired and wearing a special helmet, still managing to accumulate 7-1/2 sacks on the year.
He was a member of the Saints' famed "Dome Patrol", a four-man linebacking corps which the NFL Network ranked as the best in NFL history. In his first year as a finalist in 2010, Jackson was elected to the Pro Football Hall of Fame. Jacksons' bust, sculpted by Scott Myers, was unveiled at the Enshrinement Ceremony on August 7, 2010. He is the first member of the Hall of Fame to be inducted primarily for his contributions as a Saint.