After spending several years in the minors, Campbell was traded to the Los Angeles Kings, serving as the team's backup before joining the Toronto Maple Leafs in 2020, where he emerged as an effective starting netminder and was named an NHL All-Star in 2022.

Performing poorly with the Oilers, he was waived by the team in November 2023 and assigned to their AHL affiliate, the Condors, before being bought out at the end of the season.

During the 2010 World Junior Ice Hockey Championships, Campbell backstopped the Americans to a victory over the Canadians in the gold medal game.

In his second season within the North American Hockey League (NAHL), Campbell received the Dave Peterson Goalie of the Year Award.

[7] By the conclusion of his two seasons with the NTDP, Campbell had set a new franchise record for lowest goals-against average and most shutouts in a career.

On October 20, 2013, Campbell was recalled from Texas and made his NHL debut with Dallas, posting a 6–3 loss against the Anaheim Ducks.

[20] However, on December 28, 2015, Campbell was reassigned to the Texas Stars' East Coast Hockey League (ECHL) affiliate, Idaho Steelheads for an undetermined amount of time.

[25] Unable to progress within the Stars organization, on June 25, 2016, Campbell was traded to the Los Angeles Kings for defenseman Nick Ebert.

[30] He developed a friendship with fellow goaltender Jonathan Quick and accompanied him to the 2018 NHL Awards as his "backup", carrying a towel and water bottle with him.

Following his arrival in Toronto, Campbell experienced much success and became a fan favourite, setting several records and joining the league leaders in goaltending statistics.

[40] Campbell would remain the team's starter for the rest of the season, helping them qualify for the playoffs, where he would make his post-season debut.

[44] Following the All-Star break, Campbell's play pronouncedly declined, coinciding with ongoing struggles of his tandem partner Petr Mrazek that put the Maple Leafs' goaltending into question.

Campbell was considered a key factor opposite Vezina- and Conn Smythe Trophy-winning Lightning goaltender Andrei Vasilevskiy.

[51] With the conclusion of Campbell's contract, he was seen as one of the strongest free agent goaltenders available, and it was perceived as unlikely that the Maple Leafs would re-sign him at his desired price and term.

[52][53] Days prior to the opening of free agency it was announced that the Leafs had traded for Ottawa Senators goaltender Matt Murray, which was widely taken as confirmation that Campbell would not be returning.

Although he ultimately posted a winning record, Campbell finished the season with a .888 save percentage amid widespread criticism of his play.

[62] Campbell represented the United States numerous times over the course of his career, but his most memorable youth international competition was the 2010 World Junior Ice Hockey Championships where he backstopped the Americans to an upset victory over the host Canadians in the gold medal game.

[64] Campbell finally made his international senior debut during the 2015 Men's Ice Hockey World Championships[65] where Team USA won bronze.