The Belgian striker had previously looked likely to return to Chelsea, only for United to swoop in and agree an initial £75m ($96.5m) fee last week after becoming frustrated in their pursuit of Real Madrid frontman Alvaro Morata.
Such a deal, said to be worth an overall £100m accounting for £15m worth of add-ons and the £10m that secured Wayne Rooney's return to Goodison Park, was said to be subject to a medical and personal terms.
Those formalities have now been completed, with the Red Devils confirming Lukaku's arrival via their official website on Tuesday (10 July) and on social media using the clever hashtag "#RedRom". He has signed a five-year contract that includes the option for a further 12-month extension.
The 24-year-old, who has been working out alongside friend and new teammate Paul Pogba in Los Angeles lately, will now join up with the rest of the squad in LA as they prepare to open their latest pre-season tour of the US against the LA Galaxy at StubHub Center on Saturday.
"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," Lukaku said. "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."
Lukaku's move to Manchester sees him reunite with former Chelsea manager Mourinho, who sanctioned his permanent sale to Everton back in 2014. The pair endured something of a tumultuous relationship at Stamford Bridge, but now appear to have buried the hatchet as they embark upon a new chapter together.
"Romelu is a natural fit for Manchester United," Mourinho said. "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."
United have yet to confirm Lukaku's squad number, although it is expected that he will be handed the number nine shirt recently vacated by Zlatan Ibrahimovic. He is the second player signed by Mourinho this summer following last month's addition of Swedish defender Victor Lindelof from Benfica.