Smith attended Rancho Verde High School in Moreno Valley, California, where he played on the offensive and defensive line. He earned All-American honors by Parade, SuperPrep, PrepStar, Scout.com, and EA Sports, while also receiving numerous other All-Region honors. As a junior in 2006, he made Cal-Hi Sports All-State Underclass second team, All-CIF Central Division first team and Riverside Press-Enterprise All-Riverside County second team.
Considered a five-star recruit and described as "an amazing right tackle prospect" by Rivals.com, Smith was ranked as the No. 6 offensive tackle prospect.Scout.com, who also viewed Smith as a five-star recruit, listed him as the No. 1 offensive tackle prospect in the nation.
In his initial year at USC, Smith served as the back-up left offensive tackle behind Charles Brown, and appeared on special teams. He appeared in 10 games of the 2008 season. In his sophomore year, he became a starter at right tackle, appearing in every game of the season except for the 2009 Emerald Bowl due to academic ineligibility. He made 2009 All-Pac-10 honorable mention and CollegeFootballNews.com Sophomore All-American honorable mention.
In 2010, Smith competed with sophomore Matt Kalil for Brown's succession at left tackle, eventually losing out. He remained starting right tackle, and was first team All Pac-10. He also won the Morris Trophy award as the conference's top offensive lineman.
Smith started his rookie season as the starting right tackle for the Cowboys with Doug Free taking over the left tackle spot. Smith started every game at right tackle for the Cowboys in his rookie season, earning praise for his play and prompting the media to speculate on his possible move to left tackle in the near future.
Starting the 2012 season, Tyron has switched to starting left tackle, switching sides on the offensive line with Doug Free. On September 12, 2012, Smith was fined $15,000 for a horse-collar tackle he did during the season opener against the New York Giants. Though, little celebrated was the fact that the tackle was touchdown saving coming after an interception, which led to a goal line stand by the Dallas defense.