Midfielder links up with City's Development Squad
"I'm delighted to get the deal done, and it happening on my birthday makes it extra special. York gave me the platform to kick on so I owe a lot to them, but it's about what happens next now.
"Norwich is a huge Club and I'm looking forward to developing myself as a player here."
City boss Alex Neil added: "We're hoping Ben will be someone who can blossom into a good player in the future.
"Despite only being 18, he has already played first team football for York. That in itself suggests he's progressing quickly, and he has an athletic build already through his dad's rugby league history.
"We'll introduce him into the Under-21s to start with, and he'll be a project for us to work on."