Kennedy, who ended the 2014/2015 campaign on loan with Carlisle, has agreed a two-year deal at Brunton Park.
The midfielder's contract at the Coral Windows Stadium expires this summer, meaning he will join Keith Curle's side on a free transfer.
The 28 year-old made eleven appearances and scored three goals last season for Carlisle as he played an important part in keeping the Cumbrians in the Football League.
Before his loan move to Carlisle, Kennedy had featured twenty-six times for Phil Parkinson's team during the 2014/2015 season, scoring twice in the process.
Having moved to City from Rochdale in the summer of 2013, Kennedy made thirty-seven appearances in total for the Bantams during his time at the club.
Speaking on Twitter, Kennedy said: "I'd like to thank everybody at Bradford City for some great memories - the staff, the fans and the boys.
"I wish you all the best."
Kennedy becomes the second City midfielder to leave the club this summer after it was confirmed recently that Matthew Dolan wouldn't be offered another contract.