Last season's Premier League champions had made Lukaku their main target for the summer and he was heavily linked with a return to Stamford Bridge after four seasons at Everton.
However, when United swooped in ahead of their rivals Lukaku said he had no hesitation in joining forces with Mourinho again.
"I wanted to play for Mourinho since I was 11," he said in an interview with the Premier League Show on BBC2. "When you get another chance like that, you don't say no. I'm really grateful for the second opportunity.
"You know the expectations are really high [when you play for United]. But I was mentally prepared, I was just waiting for the opportunity to come."
While the 24-year-old was delighted to be reunited with Mourinho, the relationship between the pair hasn't always been so smooth. Upon returning to Chelsea for a second spell at the beginning of the 2013-14 season, Mourinho openly questioned Lukaku's decision to head to Everton on loan having only just returned to west London from a loan spell at West Bromwich Albion.
The Portuguese coach claimed the striker was a "young boy who likes to speak", after Lukaku said it was strange he hadn't heard from his manager.
Lukaku was an instant success on Merseyside, scoring 15 goals in 31 league appearances and made his move to Goodison Park permanent the following summer, while Mourinho ended up being sacked in December as Chelsea's title defence crumbled.
However, the disagreements between the two seem to be a thing of the past.
"[Mourinho] has always been the same, he wants the best from his players every day," said Lukaku. "He doesn't give his players the time to rest on the pitch. He wants everybody to fight in training and in the game. And off the pitch he is really like a family man - someone you can talk to, say whatever you want to say and he's going to listen to you."
The new United number nine has hit the ground running since moving to Old Trafford in the summer, netting three goals in his first three league games of the campaign as well as scoring against Real Madrid in the European Super Cup final.
United have won their first three games of the season and are yet to concede a goal but face a difficult test on Saturday [9 September] as they travel to Stoke, a ground where they have not won in their last four visits in the Premier League.