Norwell played college football at Ohio State University from 2010 to 2013. He started 39 of 50 games. During his true freshman year, Norwell was the primary backup at right tackle in 2010 and played in 11 games. He named to a Big Ten all-freshman team by Rivals.com. During his sophomore year, Norwell started 13 games and started at both the left guard and left tackle positions. He was named honorable mention all-Big Ten. During his junior season, Norwell played more downs than any player on offense with 862. The Ohio State coaches named him co-offensive lineman of the year. He helped Ohio State average 242.2 yards per game rushing, ranking 10th nationally in 2012, lead the Big Ten in scoring at 37.1 points per game, and was named first team all-Big Ten. During his senior season, Norwell was named to the preseason watch lists for the Outland Trophy and Rotary Lombardi Award. He helped lead the Buckeyes to rank fifth nationally in rushing in 2013 while setting school records for points scored, touchdowns, and touchdown passes. Ohio State also averaged an all-time program high 6.8 yards per carry and the offense was fourth nationally in the red zone percentage. Norwell was named to the first team all-Big Ten Conference for the second consecutive season. Norwell graduated in May 2014 with his degree in communications.
Despite his decorated college career, Norwell was considered a borderline NFL prospect because of lingering questions about his athleticism. Greg Cosell made the comparison to the San Francisco 49ersAlex Boone, who was also an undrafted free agent coming out of Ohio State because of their competitiveness, strength, and size. Norwell went undrafted in the 2014 NFL Draft.
Carolina Panthers
Norwell signed a three-year, $1,530,000 deal with the Carolina Panthers as an undrafted free agent on May 12, 2014.
2014: Rookie season
With the Panthers offensive line struggling, Norwell was inserted into the starting lineup in Week 7. Following Week 10, Pro Football Focus rated Norwell as the ninth best guard in the NFL, ahead of two other high-profile rookie guards, Zack Martin and Joel Bitonio. His insertion into the starting lineup at left guard helped stabilize the offensive line, and over his last six games at left guard, Pro Football Focus rated Norwell as the fourth-best left guard in the NFL. His emergence into the starting lineup helped the Panthers rank seventh in the NFL in rushing, including a league-leading 975 yards over the last five games. He also helped the Panthers to back-to-back division titles for the first time since the formation of the NFC South division. Norwell was also among the least penalized players at the position and through the entire season, did not allow a single sack and only one quarterback hit.
2015 season
Norwell picked up where he left off from his strong rookie season. Through the first three games of the season, Norwell allowed only two quarterback pressures and one sack. Through the first four weeks of the season, Norwell rated as PFF's eighth best guard in the NFL. On February 7, 2016, Norwell 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. Norwell allowed just two sacks for the season and was PFF's fifth-highest-graded run-blocking guard in the NFL.
2017 season
On March 7, 2017, the Panthers placed a second-round tender on Norwell, who was set to be a restricted free agent. On April 17, 2017, Norwell officially signed his tender with the Panthers. Norwell started all 16 games at left guard, on his to being named first-team All-Pro. He was also ranked as the third best guard in the league according to Pro Football Focus.
Jacksonville Jaguars
On March 15, 2018, Norwell signed a five-year, $66.5 million contract with the Jacksonville Jaguars with $30 million guaranteed, which at the time made him the highest-paid guard in the league. He started the first 11 games at left guard before suffering an ankle injury in Week 12. He was placed on injured reserve on November 26, 2018. As of October 2018, he was the highest paid left guard in the NFL in average salary at $13.3 million, ahead of the Raiders' Kelechi Osemele and the Tampa Bay BuccaneersAli Marpet.