Steels, who is still only 16, had been picking up rave reviews for his performances in Darlington's reserves this season.
City manager Martin Gray told the club`s official website: "I am delighted that Vinny has agreed to join us because he is a really talented young boy with a lot of potential.
"A lot of top clubs have shown interest in him over the last six months - but he feels that his future is best served by joining York."
Hartlepool-born Steels said: "I couldn't turn down the opportunity to become full-time. I also had a chance to go on trial with a Premier League club this week, but I turned it down.
"It is like a dream, really, to get a full-time club. It's fantastic," he added. "I will now work my socks off and, hopefully, impress and get in the first-team".