Mutch was a success during a loan stint at Watford earlier this season but returned to St Andrew's and made his Premier League debut against Manchester United last month.
He accepts he may have to leave St Andrew's on loan before establishing himself in the Blues squad, but the 19-year-old believes he can make a success of his Blues career.
Mutch told bcfc.com: "I'm delighted to have signed. It has taken a couple of months to sort out but now I'm happy to have a new contract at Birmingham.
"Now I'll just aim to keep on training hard, maybe look to go back out on loan again and get a few more games until the end of season.
"Then hopefully I'll come back for pre-season and try and be in and around the first team."
Source: PA
Source: PA