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.
"My vision was, 'I'm not in a rush to be a head coach. I want to do it right,'" Larson said during his introductory news conference Friday. "There's that patient endurance that goes into something like that. I'm going to learn more now. I'm going to make mistakes -- I promise you -- but that's part of the process.''
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.
"It makes me very proud to promote Brad to our head coach because he's earned it,'' Kekalainen said Friday. "It's going to be a fresh new voice for us.''
Said team president John Davidson: "There's a lot of work ahead of us, but it's exciting. We've now made this choice. We feel it's a very strong choice. The communication skills from Brad are exceptional; his love of the Blue Jackets and Columbus are way up the ladder. There was a lot of very positive things.''
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.
Larsen said he's firm but fair and believes in accountability and honesty, much like old boss Tortorella.
"I'm my own man,'' Larsen said. "I probably will handle things differently than Torts just because that's who I am and not because he was wrong and I was right, but that's who I am.''
The Associated Press contributed to this report.