Larsen, 43, signed a three-year deal to become the eighth head coach in franchise history.
He has been an assistant coach with the Blue Jackets for the past seven seasons, starting under Todd Richards for one year and then serving six seasons on the bench with Tortorella, primarily coaching the team's power play.
Larsen's only previous head-coaching experience was from 2012 to 2014 with the AHL Springfield Falcons. His team made the playoffs in both seasons.
Larsen had an eight-season NHL career as a winger for the Colorado Avalanche and Atlanta Thrashers from 1997 to 2008.
"We underwent an exhaustive process in which we looked very closely at a number of outstanding candidates to be the next coach of the Columbus Blue Jackets, and the one individual we kept coming back to throughout was Brad Larsen," general manager Jarmo Kekalainen said.
The Blue Jackets also interviewed former Arizona Coyotes coach Rick Tocchet and former Vegas Golden Knights coach Gerard Gallant -- who coached the Jackets from 2003 to 2007 -- for the opening, among others.
"Brad was one of the top young coaches in the American Hockey League when he joined our club as an assistant coach and over the past seven years has earned the respect of our players, staff and organization with his work ethic, hockey acumen and the way he treats people, and we couldn't be more pleased to introduce him as our next head coach," Kekalainen said.
Tortorella's tenure with the Blue Jackets ended last month following a disappointing season in which they finished last in the Central Division with an 18-26-12 record (.429 points percentage). He was not under contract for the 2021-22 season.