Norvell played wide receiver at Grace Preparatory Academy in Arlington, Texas, coached by former Houston Oilers tight end Mike Barber.

After graduating, because of his small physical stature, he decided to wait a year before walking on to a college football team.

He enrolled in online college courses and became an assistant coach at Grace Prep in the early fall of 1999 at the age of 17 (turning 18 in October 1999).

Norvell then walked on at Louisiana Tech in 2000 and then transferred to the University of Central Arkansas (UCA) from 2001 to 2005 and played wide receiver.

[13] With Riley Ferguson taking over as the team's starting quarterback,[14] Memphis began the Norvell era with a 35–17 victory over FCS opponent Southeast Missouri State on September 3.

[27] In 13 starts in 2016, Riley Ferguson threw for 3,698 yards and broke Paxton Lynch's single-season record with 32 touchdown passes set the previous season.

[28] After the 2016 season, co-offensive coordinator Chip Long left the Tigers to take the same position on Brian Kelly's staff at Notre Dame.

[30] On May 12, 2017, it was announced that the University of Memphis signed Norvell to a one-year contract extension though the 2021 season and gave his assistant coaches raises.

[39] After a 44–31 victory over Football Championship Subdivision opponent Southern Illinois,[40] Norvell's Tigers suffered their first loss of the season in the form of a 40–13 defeat in the rescheduled UCF game.

[42] That was followed by a 30–27 victory over #25 Navy, marking the first time the Tigers had ever defeated two ranked opponents in a single season in school history.

[48] In the 2017 American Athletic Conference Football Championship Game, the Tigers lost a hard-fought 62–55 double overtime contest to UCF.

[49] Memphis accepted a berth in the 2017 Liberty Bowl on their home field, losing the game to Iowa State by a score of 21–20.

[50] On December 5, 2017, Memphis signed Norvell to another contract extension, a five-year addition to his deal worth $13 million.

[51] The extension increased Norvell's annual pay to $2.6 million and made him the highest paid Group of 5 head coach in the country.

This time they faced Cincinnati, whom the Tigers defeated 34-24 the previous week to clinch home-field advantage for the championship game.

However, Norvell tested positive for COVID-19 ahead of the rivalry game with The University of Miami, and was not the acting head coach.

They then lost three consecutive games to ACC Atlantic foes Wake Forest, NC State, and Clemson before handily defeating Georgia Tech, rival Miami, and Syracuse.