The 18-year-old centre-back, who has been on the books at the Academy since the age of nine, has put pen-to-paper on a one-year deal, with a Club option of a further year.
Smith has impressed playing for the U18s and U23s this season and was handed a first-team squad number last month when named on the bench for the trips to Reading and Blackburn Rovers.
Speaking after signing the deal, Smith said: “To sign this deal is a huge thing for me personally. Being here since the age of nine, it’s what I’ve been working so hard to achieve for the past nine years.
“It’s a proud moment for myself and my family and I have to thank them for all the support they’ve given me over the years, along with each and every one of my coaches at the Academy as well.
“I don’t want to rest on this achievement though. I don’t want to be comfortable with where I’m at. I want to keep pushing myself.
“I want to keep progressing, keep developing and improve in all areas of my game. I just want to continue working hard in order to get to where I want to be.”