The 22-year-old has made 13 appearances for Everton this season.
Everton manager Ronald Koeman last week said the player would be allowed to leave to "get game time".
The Spaniard joined Everton on loan from Barcelona for the 2013-14 season, making the transfer permanent in 2015 for £4.3m.
Milan originally announced the move via their official Twitter account on Friday, but it was quickly deleted.
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Everton winger Gerard Deulofeu has joined Italian side AC Milan on loan until the end of the season.