The wing-back made the switch to United from Lecce on Sunday.
He told manutd.com: "It feels amazing to be part of the family. I'm very excited to get going.
"I have heard about the incredible support and I'm happy to be one of the players of United now.
"It's a huge club. It's the biggest club in England and I'm really looking forward to working with the new manager (Ruben Amorim) and I feel the system suits me really well. So I'm excited to be here."
Dorgu also said: "I think I'm going to bring a lot of intensity and physique on the pitch and a lot of energy and run(ning)."
On his mentality, the Dane continued: "For me, it's the most important thing because there's a lot of talk about and around football.
"And you really need to be strong outside of football as well.
"And, when I've been in Italy, I've lived alone. Of course, my family is visiting me a lot, but you need to be really good mentally to stay focused and being concentrated on football."
On his choice to take the No13 shirt, Dorgu said: "I had it since I came to Lecce. I think it's good to keep going with what's going good so I think, yeah, no.13 is working really good for me at the moment.
"My ambition is just to play a lot of games to be a great part of the United family and just to keep pushing and improve my potential."