Chapman, who stands at 6ft 8in in height, has put pen to paper on a one-year deal - his first professional contract - at the Proact Stadium.
The 22-year-old said: "I'm delighted to be here. It's a big step for me to get into the professional game and the hard work starts now. There are going to be eyes on me and hopefully I can deal with that."
With Richard O'Donnell leaving the club, Chapman is expected to challenge Tommy Lee for the number one jersey.
Blues boss Paul Cook said: "We've got really high hopes for him because he's got so many good attributes for a young lad."