After playing at the junior college level for Hutchinson Community College, Campbell played for the Minnesota Golden Gophers from 2013 to 2015. As a sophomore in the 2013 season, he recorded 39 total tackles, three tackles-for-loss, and one forced fumble. In the 2014 season, he recorded 75 total tackles, 6.5 tackles-for-loss, 2.5 sacks, one interception, one pass defended, and three fumble recoveries. In his final collegiate season in 2015, he recorded 92 total tackles, 6.5 tackles-for-loss, four sacks, one interception, three passes defended, and two forced fumbles.
The Atlanta Falcons selected Campbell in the fourth round of the 2016 NFL Draft. Campbell was the second linebacker drafted by the Falcons in 2016, behind LSU's Deion Jones. He was also the 16th overall linebacker drafted in 2016. On May 5, 2016, the Atlanta Falcons signed Campbell to a four-year, $2.90 million contract that includes a signing bonus of $565,528. Throughout training camp, Campbell competed to be a starting outside linebacker against Sean Weatherspoon and Philip Wheeler. Head coach Dan Quinn named Campbell the starting weakside linebacker to begin the regular season, alongside Deion Jones and Vic Beasley. He made his professional regular season debut and first career start in the Atlanta Falcons' season-opener against the Tampa Bay Buccaneers and recorded four solo tackles in their 31–24 loss. On September 16, 2016, it was reported that Campbell had sustained an ankle injury during practice. His ankle injury sidelined him for the next four games. On October 23, 2016, Campbell collected a season-high ten combined tackles during a 33–30 loss against the San Diego Chargers in Week 7. On November 27, 2016, Campbell recorded four solo tackles, made a season-high three pass deflections, andade his first career interception during a 38–19 win against the Arizona Cardinals in Week 12. Campbell made his first career interception off a pass attempt by Cardinals' quarterback Carson Palmer, that was originally intended for tight end Jermaine Gresham, to seal the Cardinals' victory in the fourth quarter. Campbell was inactive during the Falcons' Week 16 victory at the Carolina Panthers after suffering a concussion the previous week. He finished his rookie season in 2016 with 48 combined tackles, seven passes defensed, one forced fumble, and one interception in 11 games and ten starts. The Atlanta Falcons finished first in the NFC South with an 11–5 record in 2016 and earned a first round bye. On January 14, 2017, Campbell started his first career playoff game and recorded four combined tackles during a 36–20 win against the Seattle Seahawks in the NFC Divisional Round. The following week, the Falcons defeated the Green Bay Packers 44–22 in the NFC Championship Game. On February 5, 2017, Campbell started in Super Bowl LI and recorded four total tackles as the Falcons were defeated 34–28 by the New England Patriots in overtime.
On February 8, 2017, the Atlanta Falcons fired defensive coordinatorRichard Smith after they lost a 28–3 lead in Super Bowl LI and allowed the New England Patriots to score 31 points in the second half of the game. On February 10, 2017, the Atlanta Falcons announced their decision to promote secondary coach Marquand Manuel to defensive coordinator. Campbell entered training camp slated as the starting strongside linebacker after Vic Beasley was moved closer to a edge rushing defensive end role. Head coach Dan Quinn named Campbell the starting strongside linebacker to begin the regular season, alongside weakside linebacker Duke Riley and middle linebacker Deion Jones. On September 17, 2017, Campbell recorded eight combined tackles, deflected a pass, and made his first career sack on Packers' quarterback Aaron Rodgers during a 34–23 victory against the Green Bay Packers in Week 2. In Week 10, he collected a season-high 13 combined tackles in a 27–7 victory against the Dallas Cowboys. Campbell started in all 16 games in 2017 and recorded 92 combined tackles, four pass deflections, and two sacks.
2018
Campbell returned as the starting strongside linebacker to begin 2018, along with Duke Riley and Deion Jones. He played in 16 games with 13 starts, finishing with a team-leading 94 combined tackles, and 1.5 sacks.
2019
In Week 4 against the Tennessee Titans, Campbell recorded a team-high 17 tackles in the 24–10 loss. In Week 11 against the Carolina Panthers, Campbell recorded a team-high 11 tackles and intercepted a pass thrown by Kyle Allen in the 29–3 win. In Week 15 against the San Francisco 49ers, Campbell forced a fumble on running backMatt Breida which he recovered in the 29–22 win.
Arizona Cardinals
On April 3, 2020, Campbell signed a one–year contract with the Arizona Cardinals.