The England Under-19 international defender last season stepped up to Saints' Under-21s side, where he formed an impressive centre-back partnership with Jack Stephens.
Stephens penned a new deal at St Mary's earlier in the summer and Turnbull has now followed suit, committing his future to Mauricio Pochettino's club.
"I'm really pleased and I think it's a great opportunity now for me to keep driving and push on into the first team," the 18-year-old told the club's official website.
"As you can see with the likes of James Ward-Prowse, Luke Shaw, and Jack Stephens - who signed a new contract recently - the club is trying to bring youth through, and that's really good for us so hopefully now I can follow their steps.
"It's a relief that I've been offered a new contract, and now I can focus on football. My scholarship has gone very quickly, but I am pleased with how I've progressed, and I've just got push on and on now to get into the first team."