Norvell is the son of Tonja Hall and Zachary Norvell, who played basketball in college at Northeastern Illinois and New Mexico State and coaches at DuSable High School. Growing up, the younger Norvell was an accomplished baseball player but decided to quit to focus on basketball. At Simeon Career Academy, Norvell played limited minutes as a freshmen behind Jaylon Tate and Kendrick Nunn. As a junior, Norvell averaged nearly 13 points, four rebounds and three assists per game and was a Chicago Tribune All-State special mention selection in 2015. He played some time at point guard due to injury problems. He scored 53 points in an AAU game for Mac Irvin Fire in Las Vegas in July 2015, increasing his recruiting stock. Norvell ended up committing to Gonzaga, choosing the Bulldogs over offers from Florida State, Georgetown and Iowa State. Norvell was No. 76 in ESPN’s Top 100 rankings and was nominated for the McDonald’s All-American game.
College career
Norvell underwent leg surgery before arriving at Gonzaga for his freshman season. Norvell redshirted during his first season at Gonzaga, partially so he could recover from his leg injury. Despite his redshirt, he was allowed to play an exhibition game against West Georgia, where he was able to score 18 points. Coming into his redshirt freshman season, Norvell was named to the Julius Erving Award watch list. During his redshirt freshman season, Norvell was able to become a breakout star of the NCAA tournament, leading his team by scoring 21.5 points per game during the first 2 games of the tournament. He was also able to make a game tying three-pointer against UNC Greensboro and recorded his first career double-double against Ohio State with 28 points and 12 rebounds. On the season, Norvell averaged 12.7 points, 3.9 rebounds, and 2.4 assists per game. He was named West Coast Conference Newcomer of the Year. Coming into his sophomore season, Norvell was named to the Preseason All-WCC Team. He was named to the preseason John R. Wooden Award and Jerry West Award watchlists. At Gonzaga, he was known by the nickname "Snacks". He posted a career-high 28 points against Creighton on December 1, 2018. He was named to the 2018–19 All-West Coast Conference first team along with teammates Rui Hachimura, Brandon Clarke and Josh Perkins. Following the season, he declared for the 2019 NBA draft. He was invited to the NBA Draft Combine. On May 9, he announced his intention to remain in the draft.
Norvell went undrafted during the 2019 NBA Draft. On July 1, 2019, Norvell signed with the Los Angeles Lakers to a two-way contract. On October 25, 2019, Norvell made his debut in NBA, coming off from bench in a 95–86 win over the Utah Jazz with a rebound. Norvell was waived on December 11, 2019.
On February 8, 2020, Norvell signed a 10-day contract with the Golden State Warriors. Although he had appeared in a pair of games for the Lakers, Norvell scored his first points on February 8, when he posted seven points, four rebounds, two assists and two steals in a 17-minute plus 10 debut for the Warriors against the Los Angeles Lakers.
Santa Cruz Warriors (2020–present)
On February 21, 2020, the Santa Cruz Warriors announced that they had acquired Norvell from the South Bay Lakers for the returning right to Juan Toscano-Anderson and a 2020 1st-round draft pick in 2020 NBA G League Draft. In his debut for Santa Cruz, Norvell scored a career-high 34 points shooting 7-of-12 from behind the arc while also contributing five rebounds and four assists in a 128-122 loss to the South Bay Lakers.
