Lukaku arrives at Old Trafford on a five-year deal and has cost Manchester United an initial £75million, rising to £90m with add-ons.
The Belgium international will link up with his former Chelsea manager Jose Mourinho.
And the United boss is looking forward to working with the 24-year-old again.
Mourinho said: "Romelu is a natural fit for Manchester United. He is a big personality and a big player.
"It is only natural that he wants to develop his career at the biggest club.
"He will be a great addition to the group and I know they will make him very welcome. I am really looking forward to working with him again."
Wayne Rooney left United yesterday to complete an emotional return to his boyhood club Everton.
Lukaku spent four years at Goodison Park - including an initial loan spell - and went on to score 87 goals in his 166 Everton appearances.
He became the Toffees' record goalscorer in the Premier League last term but admits he couldn't turn down the opportunity to join United.
Lukaku said on the deal: "I would like to start by thanking Everton and the fans for the last four wonderful seasons, I have made some special friends and we have shared some amazing moments.
"However, when Manchester United and Jose Mourinho come knocking at the door it is an opportunity of a lifetime and one that I could not turn down.
"You could see the fight, determination and the spirit in this team during the Europa League final and I want to become a part of that.
"I cannot wait to run out at Old Trafford in front of 75,000 fans but before that pre-season is where the hard work starts and I am looking forward to that first training session."
Source: Daily Express