Lukaku, 24, will reunite with former Chelsea manager Jose Mourinho at Old Trafford for a reported £75 million fee.
United had targeted Real Madrid forward Alvaro Morata to help fill the void left by last season's top goalscorer Zlatan Ibrahimovic, who did not have his contract renewed following a serious knee injury suffered in April.
But Mourinho and United have turned to Belgium international Lukaku to try to fix their scoring woes, having only found the back of the net on 54 occasions in the Premier League last term – the lowest tally among the top seven teams.
Although Chelsea made an attempt to lure him back to Stamford Bridge by matching United's bid, the Red Devils confirmed they have reached a deal for Lukaku, who must still agree personal terms and pass a medical.
#MUFC is delighted to announce a fee has been agreed with Everton for the transfer of Romelu Lukaku, subject to a medical & personal terms. pic.twitter.com/O7oQJWzYHo — Manchester United (@ManUtd) July 8, 2017
Lukaku spearheaded Everton to seventh position in 2016-17 with 25 Premier League goals as he finished second behind Golden Boot winner Harry Kane.
The former Chelsea youngster spent a year under Mourinho at Stamford Bridge before he was sold in 2014.
Following an initial loan spell at Everton, Lukaku scored 53 Premier League goals for the Toffees and 71 in all competitions.
The former West Brom loanee hit 26 goals in all competitions last season were the most by an Everton player since Gary Lineker's 40-goal haul in 1985-86.
Since debuting for Belgium in 2010, the former Anderlecht star has scored 20 goals in 57 international appearances.