Lukaku is reunited with United boss Jose Mourinho, who sold the striker to the Toffees in 2013 during his time in charge of Chelsea.
The Belgium international wasn't Mourinho's first choice, but was targeted after the Red Devils were priced out of a move for Real Madrid marksman Alvaro Morata.
Lukaku is a proven goalscorer in the league having reached double figures in each of his last five seasons in the top tier of English football, with 25 goals coming in the 2016/17 campaign alone.
The 24-year-old has penned a long-term deal at Old Trafford until 2022, with an option to extend for another 12 months.
"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," he told United's official website.
"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."
Mourinho added: "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."