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The club have announced that the 40-year-old has signed a two-and-a-half-year contract following the dismissal of Mowbray last month.
Chief executive Neil Bausor told the club's official website: "We are delighted that Aitor has decided to further his coaching career with Middlesbrough as our head coach.
"He brings with him some fantastic experience as a player and as a talented young coach. We are all excited about working with him."
Karanka, who left the Madrid coaching staff in the summer following Mourinho's return to Chelsea, has become Middlesbrough's first foreign manager in their history.