Addison attended Tarrant High School outside of Birmingham, Alabama. At Tarrant, he lettered in varsity football and basketball for four years. He originally played running back, but was moved to quarterback after the injury of the original starter. After suffering a broken hand on his throwing arm, he changed positions to defensive end. He was recruited lightly as a high school senior and chose to enroll in Northeast Community College in Booneville, Mississippi after graduation. After playing at Northeast Mississippi Community College for two years, Addison signed to play with Troy University. After redshirting his first year in 2008, he began seeing playing time in 2009 as a reserve player at the defensive end position. Despite being a reserve player, he saw action in all 13 games during the season and recorded 2.5 sacks and 6.0 tackles for loss. In 2010 during his senior season, Addison broke out as a star player for Troy. He recorded 10.5 sacks, 15.5 tackles for loss, and 3 forced fumbles on the season. He was named to the All-Sun Belt Second Team following the end of the season. Addison began receiving attention from various NFL teams for his performance that year, but was never drafted.
Professional career
Chicago Bears
Addison was signed on July 26, 2011 by the Chicago Bears as an undrafted free agent. He was cut by the Bears on November 21, 2011 to free up space on the 53-man roster for veteran players to cover the injuries picked up by long snapperPatrick Mannelly and quarterback Jay Cutler in the previous day's 31-20 victory over the San Diego Chargers. He had only played in two games with the team.
Indianapolis Colts
Addison was claimed off waivers by Indianapolis Colts on November 22, though the Tampa Bay Buccaneers had also placed in a claim for Addison. On October 1, 2012, Addison was waived by the Colts, but added to the practice squad the next day.
Washington Redskins
Addison was signed off the Colts' practice squad by the Washington Redskins on October 9, 2012. After playing five games with the Redskins, he was waived by the team on November 29. He was signed to the practice squad the next day.
Carolina Panthers
Addison was signed on December 4, 2012 by the Carolina Panthers from the Redskins' practice squad. On June 18, 2014, he signed a two-year contract extension. Through the first five games of the 2014 season, Addison led the Panthers with five sacks and pass rush productivity. Addison contributed to the Panthers in 2015 with 6.0 sacks on one of the league's best defenses. On February 7, 2016, Addison was part of the Panthers team that played in Super Bowl 50. In the game, the Panthers fell to the Denver Broncos by a score of 24–10. On February 26, 2017, Addison signed a three-year contract extension with the Panthers after leading the team with 9.5 sacks in 2016. In week 3 of the 2019 season against the Arizona Cardinals, Addison sacked rookie quarterback Kyler Murray 3 times in the 38-20 win. Addison recorded two more sacks against the Houston Texans' Deshaun Watson the following week in a 16-10 win.
Buffalo Bills
On March 27, 2020, Addison signed a three-year contract with the Buffalo Bills.
NFL statistics
Regular Season
Personal life
Addison is a member of the Rho Delta Delta chapter of Omega Psi Phi fraternity at Troy University. Addison is a Christian. His brother, Gjamal Antonio Rodriqcus, was shot and killed on October 30, 2019.