Lukaku, who enjoyed a successful season-long loan at Goodison Park last term, has put pen to paper on a five-year contract after the clubs agreed a fee of £28 million.
Everton confirmed the news at a press conference featuring the Belgium international and manager Roberto Martinez on Wednesday.
Speaking about the move, Lukaku said: "I am really excited about rejoining Everton.
"I had a fantastic experience last season and a great relationship with the manager, the chairman, the staff, the players and the fans.
"I can't wait to get started again and I'm looking forward to a successful season."
Martinez, meanwhile, is thrilled to have brought Lukaku back to Goodison Park and expects the 21-year-old to develop further on Merseyside.
"Welcoming Romelu Lukaku back to Everton on a permanent basis is the news that all Evertonians wanted to hear," said the Spaniard.
"We know that Romelu is still a young man and the potential that he has is quite unique, and we are desperate to see him enjoying his football and to watch him grow as a footballer in the years to come.
"The arrival of Rom is more than just a signing, it's the fruition of a lot of hard work to get the player we wanted.
"This is a big moment for Everton's history and the perfect way of getting the squad ready for the start of the season."
Lukaku scored 15 goals in 31 Premier League appearances for Everton last season, helping the Merseyside outfit to a fifth-place finish in Martinez's first campaign in charge.
The striker, who made just 10 Premier League appearances for Chelsea after joining from Anderlecht in August 2011, had long been considered surplus to requirements at Stamford Bridge.
Chelsea boss Jose Mourinho sent Lukaku out on loan last term despite publicly complaining about the quality of forwards at his disposal, and the arrivals of Diego Costa and Didier Drogba this close-season had pushed the 21-year-old further down the pecking order in west London.
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