"We have one of Europe's most exciting prospects," acting chief executive Robert Elstone told the club website.
"This is fantastic news for everyone connected with the club. He will have a huge part to play at Everton over the next five years.
"I spoke with chairman Bill Kenwright and manager David Moyes shortly after concluding the deal and they are delighted we have managed to secure his services.
"It came late on, like a lot of the big deals in the Premier League, but he's with us and we look forward to welcoming him to Goodison."
The deal ends a frustrating summer transfer window for Everton, which had led to Moyes coming under pressure following his failure to attract players to Goodison Park.