Davidson agreed to a buyout of his St. Louis contract in early October after a change in the Blues' ownership.
"John will have full authority and autonomy over the competition side of the business," said team president Mike Priest during a Wednesday news conference.
Davidson is largely credited for his patience and expertise in building the Blues into Western Conference contenders, surrounding himself with a talented front office and focusing primarily on the draft to build one of hockey's best young cores. St. Louis won the Central Division last year, finishing with 109 points.
He also is one of the most connected people in hockey and is known for his ability to sell the game, an important distinction in Columbus where frustration is at an all-time high after another dismal season. He joins a growing front office that also includes Priest, senior adviser Craig Patrick and general manager Scott Howson.
Davidson said there are no negatives about taking the job in Columbus.
"You think about the organization itself and how much they want to win ... you can see they want something very, very badly," he said. "The ownership group is just a great group."
The Blue Jackets traded captain Rich Nash this summer following a season in which they finished last in the NHL with 65 points, 44 behind Davidson's Blues.
Before joining the Blues, Davidson was a Hall of Fame broadcaster with MSG, and there was speculation that his departure in St. Louis might bring him back to the television booth, a career choice many hockey fans would have applauded considering his popularity on television. The former goalie instead chose the challenge of rebuilding the Blue Jackets.
"This is going to be a really, really good hockey club as we march along," Davidson said.