The 17-year-old left-back, who has been with the club since he was 12, made over 100 appearances for the Reds' Under-18s and Under-21s during his two-year scholarship before signing a one-year contract to join up with Danny Wilson's squad.
"I'm very happy just to sign. It's my home-town club, I've lived here all my life," Smith told the club's official website.
"It's a club close to my heart and to sign a professional deal here makes me very happy."
He added: "My aim for next season is to come back flying, fit, healthy and strong. I'm going to show Danny Wilson what I'm about. I want to get on that pitch week in, week out."
Teenage strikers Nana Boakye-Yiadom and George Maris both signed their first professional contracts with the club last week.