Karanka, 40, a former defender who won one Spain cap, played for Athletic Bilbao and Real Madrid in a 13-year playing career and was in the Real team that won the Champions League in 2000.
He spent three years as Mourinho's assistant at the Bernabeu until Mourinho left Real for Chelsea in June.
"He brings with him some fantastic experience as a player and as a talented young coach. We are all excited about working with him," club chief executive Neil Bausor said after securing the coach on a two-and-a-half-year contract.
Karanka was linked with the vacant managerial post at Premier League bottom-side Crystal Palace, but instead opted for Middlesbrough, who are currently 16th out of 24 teams in the English Championship (second tier).
Middlesbrough have been under the guidance of caretaker manager Mark Venus since the club parted company with Tony Mowbray on October 21.
(Reporting by Mike Collett; editing by Amlan Chakraborty)
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