Aged 16 years and 268 days, Mutch became Blues' second youngest debutant ever - just behind the legendary Trevor Francis - when he appeared as a substitute in a Carling Cup tie against Southampton in August.
Mutch told the Birmingham Mail: "It's a step further in my career. I am looking forward to next season after a big year this season. It has been hard with the injury but I am just looking to next season and progressing on.
"I think I will come back stronger and hopefully be in the team next season. My target is to get in the first team next year, go away with them in pre-season and hopefully get a few games under my belt."
Academy Manager Terry Westley added: "We have an outstanding prospect on our hands - one of the top young midfielders in the country and we're delighted that he's decided to sign a two-and-a-half year contract."
Teenage defender Jacob Rowe has been also been offered a one-year professional contract by the club which he is expected to sign following the end of his academy scholarship in June.
The 18-year-old centre-half won the club's academy player of the year award and his performances have helped him earn the contract.
Academy coach Steve Spooner said: "Jacob is a great example to all the young players at the club that if you apply yourself and if you have a desire to work you can earn a professional contract.
"If anyone deserved one on sheer determination to improve it's him. He knew what he was short of and tried to do something about it by working on his weaknesses.
"The aim now is get rid of those weaknesses that would prevent him getting in the first team, so there's always a bar you've got to jump over to get to the next level."
Rowe's fellow second year academy scholars Robert Gradwell, Dean Lyness, Jack Rutter, Jamie Sheldon and Shaun Timmins have not been offered professional terms.