The Spaniard takes charge of his first club with Boro just five points clear of the Sky Bet Championship relegation zone, with Mark Venus standing down following his caretaker manager stint.
Karanka had been linked with the vacant job at Barclays Premier League outfit Crystal Palace but instead opted to move to join Boro on a two-and-a-half-year contract.
"It is a very important day for me," said Karanka at his unveiling.
"This is my first job and it is the best thing that I can do because I have found a club like a family with big facilities with a big stadium, with big supporters, it's a very important day for me.
"It is my time. I have been, for three years, with Jose Mourinho and I think he supported me every day. I learned with him and his staff and I'm ready (now)."
Karanka, who left Real Madrid during the summer, spoke in glowing terms of Mourinho, who persuaded the 40-year-old to coach Middlesbrough.
"You can learn everything on the pitch and off the pitch and the changing room. He's the one," Karanka added.
"He's the person who's supported me for months. He recommended me to come here because he believes in this project, like me."
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- Jose Mourinho