United sold Keane in January 2015 to Burnley folllowing a successful loan spell with the club, inserting a 25% sell-on clause into the 24-year-old's contract.
Reports suggested that they were also able to trigger a buy-back clause should they wish to reclaim the England man, something which Jose Mourinho looked interested in doing earlier in the year.
Keane made 35 Premier League starts for Sean Dyche's Burnley last term and broke into the senior England squad as a result of his outstanding performances.
Mourinho has previously been open about his plans to strengthen his defensive options, with Keane's improved standing making him a prime target.
Keane, though, has expressed his delight in his move to Goodison Park, where he has signed a five-year deal.
“I’m absolutely delighted to be at Everton, a fantastic football club with passionate fans and a great tradition and I can’t wait to come into training tomorrow to meet all the lads,” He said.
“I watched a lot of Everton last season and I believe I really suit how the team likes to play. I feel like this is a great place to come and continue my development as a player.