The out-of-contract 26-year-old has penned a two-year deal with the Bantams after rejecting fresh terms at League Two side Rochdale.
Kennedy made close to 200 first-team appearances for Dale having signed on a free transfer from Darlington in August 2009 and was a virtual ever-present in the side last season.
He is the first new face at Valley Parade since the Bantams secured promotion to League One via the play-offs.
Speaking in late June, Dale boss Keith Hill was resigned to losing Kennedy's services.
"I've spoken with Jason and it's highly unlikely that he's going to be signing," Hill told the club's official website.
"It was important for me as a manager when I came back to the football club that I retained Jason for the 18 games that I was here.
"I'm glad he stayed because he did have an opportunity to possibly leave. He was tremendous for me when I came back and I'm happy for him to be signing for another football club, whether it is in this division or a league above.
"As long as his family is happy and the location is suited to him and his family."