Jackson redshirted for the Tigers in 2004. As a redshirt freshman in 2005, he earned a spot on the Freshman All-SEC team by the league’s coaches and the Sporting News. He recorded thirteen tackles and two sacks and added five quarterback pressures. As a sophomore, in 2006, Jackson was a Second-team All-SEC selection. He was a starter at left defensive end and recorded 37 tackles. He also had 8.5 sacks, six pressures and 10.5 tackles for a loss. Jackson caused and recovered a fumble, broke up four passes and caught an interception. As a junior, in 2007, Jackson started thirteen of fourteen games at left defensive end. He totalled 36 tackles with 3.5 sacks, 4.5 stops for losses, and twelve quarterback pressures. Jackson caused a fumble and ranked second in the NCAA among defensive linemen with ten pass break-ups. As a senior, in 2008, Jackson earned All-SEC Second-team again. He recorded 36 tackles that included 4.5 sacks, 10.5 stops for losses, and seven quarterback pressures. He recovered a fumble and deflected four passes. In total, Jackson started 38 of 53 games at LSU, recording 122 tackles with 18 pass deflections, one interception, two forced fumbles, and a pair of fumble recoveries. He ranks eighth in school history with 18.5 sacks and is eleventh with 27 stops for losses.
Although having played in a 4-3 alignment at Louisiana State, Jackson was considered an ideal 3-4 defensive end. He drew comparisons to Anthony Weaver. Jackson was chosen by the Kansas City Chiefs in the first round with the third pick overall.
Kansas City Chiefs
Jackson was drafted with the third overall selection by the Chiefs, who looked to implement him as defensive end into their new 3-4 defense. Jackson remained unsigned at the beginning of the Chiefs' training camp session and did not travel with the team to River Falls, Wisconsin. The holdout ended on August 7 as he was signed to a five-year contract reportedly worth $57 million with $31 million guaranteed. Tyson played in all 16 games of his rookie season and had 38 tackles with two pass deflections. In 2010, he recorded 31 total tackles and one sack. In 2011, Jackson had only one sack though he also had a career record of 55 tackles.
On March 11, 2014, Jackson signed a five-year $25 million deal with the Atlanta Falcons. In the 2016 season, Jackson and the Falcons reached Super Bowl LI, where they faced the New England Patriots on February 5, 2017. In the Super Bowl, Jackson had one total tackle as the Falcons fell in a 34–28 overtime defeat. On March 9, 2017, Jackson was released by the Falcons.
