The 23-year-old goalkeeper, who started against Manchester City in Wigan's FA Cup final victory at Wembley, has followed Roberto Martinez to Goodison Park
The 23-year-old, who was brought to Wigan Athletic on loan by Roberto Martinez in January, has signed a five-year contract with Everton.
Joel was also part of Spain's squad for its European Under-21 Championship campaign earlier this summer and is now reunited with Martinez at Goodison Park.
Joel, who started for Wigan in the club's FA Cup final win over Manchester City, kept four clean sheets in his 12 outings for the Latics and conceded 17 goals.
"He arrives to challenge Everton's established custodian Tim Howard for a place in Roberto Martinez's starting line-up and is traveling with the squad to their Austria training camp," read a statement from Everton.
Earlier on Tuesday, Everton also completed a move for defender Antolin Alcaraz, who signed a two-year deal after his contract with Wigan expired at the end of June.