The midfielder, 18 next month, has put pen to paper on a one-year deal which keeps him at Brunton Park until the summer of 2014.
Blues boss Greg Abbott told the club's official website: "In Jack Lynch we've seen the type of midfield player that we possibly haven't had for a while.
"He is fantastic in the way he chases the opposition down and in the way he tries to make sure he wins his battles.
"He's extremely tenacious, he has an excellent range of passing and he is one who brings a really competitive edge to his game. That gives us quite a lot to work with."
Lynch has spent two years as a trainee at Carlisle and has frequently trained with the first-team squad throughout his time at the club. He has also been a regular in the Blues' reserve sides.