The 18-year-old has committed himself to the Cumbrians until the summer of 2014 following the successful completion of his two-year YTS programme.
Salmon enjoyed a taste of first-team action with late-season substitute appearances against Bournemouth and Colchester for Greg Abbott's men.
"Even though I've signed, it still hasn't really sunk in," he told Carlisle's official website. "I think that will only happen when I come back.
"It is nice to have it done. It's what you want to achieve when you first come to the club and it's a great feeling when it actually happens. I just want to get this break over with and get back to work.
"I've had to put a lot into my two years to try to get to this stage but I know that the really hard work starts now. I have to prove that I'm good enough to perform for the first team. Getting my debut, home and away, has been massive for me."