The 20-year-old becomes the club's 11th signing this summer and has penned a four-year contract.
"He is another important player and I am expecting a lot from him," Boro boss Aitor Karanka told the club's official site.
"I've known him since he was a kid. He went into the national team just after I left, but I know all about him and what he can do.
"His level is higher than he showed last season, but in the right environment I'm hoping that he will show what he is capable of."