The 19-year-old has agreed a three-year deal at the Reebok Stadium and becomes the club's third summer signing following the arrivals of Martin Petrov and Robbie Blake.
Manager Owen Coyle told the club's official website: "He is an exciting young player who has undoubted quality and he will bring that into our mix. I think that we have a real talent on our hands.
"I have said before that when we are investing money in transfers that I want to do it with young, talented players. He isn't the finished article yet - he's a young player making his way - but you don't get through at Real Madrid without having a bit about you."