Hamilton, 20, is yet to make a senior appearance for the Red Devils, but was in the squad for their FA Cup victory against Huddersfield last term.
The Scot said, “I'm delighted to come here.
“I've had a look around the place and all the people that I've met at the Club seem really great, so it's an exciting time for me.
“To come here and play proper men's football is going to be great and I can't wait. It will be a big difference from playing Academy football.
“It's something I need in my development and I'm really grateful for the opportunity to come here.
“I've had a conversation with the Manager and we're both keen for me to get started, so I'm really excited.
“I'm a type of player that will give everything. I've got quite a lot of energy, I like to go box-to-box and get involved. I'll try and perform to the best of my ability."