Broadhead, a product of the youth set up at the League Two outfit, has put pen to paper on a two-and-a-half-year deal after impressing in the youth team and reserves.
The defender, 18, made his first-team debut for Paul Cook as a substitute in the recent 6-1 win over Hartlepool in the FA Cup first round at the Proact Stadium.
He told the club's official website: "It feels great to get something you've worked so hard for. I appreciate how lucky I am to get a chance at Chesterfield and I'm now looking to repay the faith people have shown in me.
"The youth-team manager Dave Bentley has had a big influence on me and given me the captaincy this season."
Bentley said: "The contract Jack has been given is just reward for the hard work he has put in. He's taken his game forward this season and will hopefully continue to do so."