Lukaku joined Manchester United in a £75million deal from Mersyside club Everton, agreeing to a five-year contract.
He appeared to be set for a move back to Chelsea, having left the club while Mourinho was manager.
But the Stamford Bridge outfit lost out to Man United.
Discussing the arrival of Lukaku, 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.”
Lukaku is set to train with United for the first time this evening and admits he cannot wait to get started.
“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,” he added.
“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.”
See also
Conte urges Abramovich to sign 24-year-old PSG keeper
Chelsea offer £26.5m for Keita as Juventus, Milan and Inter back out
Lukaku explains why he chose United over Chelsea