He will take the place of Mike Priest, who will concentrate only on the business side of the franchise.
The Blue Jackets had the worst record in the NHL last season with a mark of 29-46-7 for 65 points.
Davidson, a member of the Hockey Hall of Fame as a broadcaster, served as president of the Blues from 2006 until earlier this year. He helped transform the team into one of the best in the league last season.
A former goaltender for the Blues and New York Rangers, he retired in 1983.
Source: Associated Press