Grant left Stoke City this summer for United.
"I think there may have been some surprise, but maybe not from those who have seen me play," said Grant. "I pride myself in the way I conduct myself and that's probably part of the reason why I'm here.
"I got a phone call and was asked if it was something I would be interested in. If it's Man United, the answer is pretty short and sweet.
"I was a big United fan growing up. You have to try to hide that at other clubs. You have kids and you move clubs and get around the country and you become a fan of whatever club you're playing for. But the truth is I was always a Man United fan.
"I imagine quite a lot of players do say that coming here. But I was. My favourite keepers were Les Sealey, Jim Leighton, Peter Schmeichel obviously.
"I loved watching Edwin van der Sar and even now David is still one of my favourite goalkeepers to watch.
"I loved watching all of those guys and I'm excited now to hopefully have an opportunity play for the football club and in some small way be a part of it."