Wright played college football for the Texas Longhorns, earning consensus All-American honors in 2005 and a National Championship.

After seeing limited action as a sophomore, he was a first-team all-district selection as a junior after registering 92 tackles, nine quarterback sacks and a blocked extra point attempt.

He was a finalist for the Greater Houston Touchdown Club Player of the Year award that season during which he posted 104 tackles, six sacks, three fumble recoveries and two blocked point-after attempts in 2001.

Wright played in the 2002 U.S. Army All-American Bowl alongside fellow Texas Longhorns Kasey Studdard and Justin Blalock.

Considered a five-star recruit by Rivals.com, Wright was ranked second among defensive tackle prospects in the nation (behind Haloti Ngata).

He earned Big 12 Defensive Freshman of the Year honors from the league's coaches, Fort Worth Star-Telegram, Houston Chronicle and The Sporting News.

He earned second-team All-Big 12 honors from the Associated Press, the conference coaches, The Austin American-Statesman and the San Antonio Express-News.

He was a finalist for the Lombardi Award and tabbed First-team All-America by the Walter Camp Football Foundation and the Associated Press.

Despite being widely regarded as a very good pro prospect and one of the best defensive tackles in the nation at Texas, Wright fell all the way to the seventh round and was selected by the Miami Dolphins with the 226th overall pick in the 2006 NFL draft.

Fully recovered from shoulder surgery, Wright practiced at defensive end as the backup to Vonnie Holliday during the team's April minicamps.

[5] Wright signed with the Saskatchewan Roughriders on October 27, 2010 as an injury replacement at the end of the 2010 season.,[6] but was waived prior to the 2011 season.

During his tenure, the Bearkats posted a 46–12 overall record, a 31-4 Southland Conference mark, reached the semifinals of the NCAA Division I Football Championship Subdivision (FCS) playoffs three times and the quarterfinals in another year.

He ranked among the nation's top 10 with 19.0 tackles for loss as a senior and finished his career with a school- and FCS-record 84.0 TFLs before being selected by the Oakland Raiders in the second round of the 2018 NFL Draft.

Three of his defensive linemen — Lorenzo Dantzler, Jaylon Haynes and Brandon Matterson — earned honorable mention all-conference recognition, while Christian Clayton was named to the 2020 C-USA All-Freshman Team.