The 17-year-old, who made his senior debut earlier this season, is currently a second-year scholar at the club's Academy but has penned a deal which will keep him at St James Park until 2016.
It means the diminutive striker will continue to play for the club's Under-18s before graduating to the first-team squad in the summer.
He told the club's official website: "I'm over the moon - I can't say I was expecting it yet. I've been working hard and I've kept doing what I do, and I was expecting that at the end of the year when players normally get a decision that I might have done enough.
"So it has come as a surprise and I'm really grateful for it."
Jay made his City bow as a late substitute in a Johnstone's Paint Trophy tie with Wycombe in September before making his first Football League start against Southend last month.