Kennedy impressed Blues boss Keith Curle during an 11-game loan spell from Bradford this season and he is set to return to Brunton Park permanently when his contract with the Bantams expires in the summer.
The 28-year-old has signed a two-year contract with the Cumbrians and Curle said: “Jason came in at the end of last season and he did exactly what we expected him to do.
“The fans responded well to him because they could see the drive and passion he brings with his game.
“People like that. He has been excellent to work with and we’re delighted that he’s accepted the offer. He’s the kind of player I know I can work with and you can see in his eyes that he wants to be here and he wants to help this club do well.
“I know people can get frustrated when things are quiet through the summer months but this is an example of how we have to keep doing the leg work to get the deals we want to conclude over the line.
“This is the first of our signings and I continue to talk to other targets, and their representatives, as I look to build a squad to push us on next season.”