It marks the second time Lukaku has worked under Mourinho, with the pair enjoying a somewhat uneven relationship when the 24-year-old was trying to break into the first team at Chelsea.
When asked if Mourinho was a big factor in his decision to join United, Lukaku replied: "Yeah, he was. To be fair, when I was starting to learn stuff about the game I knew that he was the manager I wanted to play for if I ever had the chance.
"I had the opportunity to work under him when I was 20 at Chelsea. It didn't go how I expected it to happen but we have moved on from there.
"We have a brilliant relationship. He knows that I will go through a brick wall for him.
"I am really excited to work under him and to improve. I want to challenge for trophies and be in the dressing room with great players but also great characters. It is something that I wanted and it is going to help me to get better."
Lukaku was widely expected to leave Everton this summer after turning down a new contract but it was assumed by most that Chelsea, not United, were in pole position to sign him.
