The 23-year-old midfielder has signed a four-year contract after passing a medical, the club's official website said.
Boss Tony Mowbray said: "I'm delighted to welcome Borja to the club.
"From a footballing point of view he possesses many of the attributes I like in a player."
Mowbray added that despite a record fee Valero was not guaranteed a place in the team.
"Borja can link up the play from back to front and he will enhance the excellent midfield options we already possess."