Miller told MUTV:
"It's great really. I was looking forward to it but obviously I had a bit of time to go at Celtic but it's great to finally be here. I was just being professional and seeing it out, and looking forward to the new start really.
"It's going to be exciting here and I'm definitely looking forward to it. I can't wait to meet the lads. They're world class players. You can learn from them and I'm hopeful that I will.
"Playing for United will be a great feeling, having supported them as a boy.
"It was nice to meet Roy, and I knew John O'Shea already from the youth squads. It's nice to come here knowing a few people and have a few familiar faces.
"I'm looking forward to the games and also looking forward to training which starts back on Sunday. I'm looking forward to getting back in the swing of things."