The 19-year-old forward will now remain with the Championship side until June 2023.
There is no option to buy in the contract - which was signed on Thursday morning.
He will now follow in the footsteps of his father Rory Delap, who made 208 appearances for Stoke during his playing career and is now a first team coach.
In his first official interview for the club, the England U19 international said: "Obviously it's a brilliant feeling (to be here).
"I've known and been around this club for a long time and to finally get the deal done and over the line, I'm buzzing. I can't wait to get started."