Karanka takes on the role following a stint in Jose Mourinho's coaching staff at Real Madrid, which he left in the summer after the Portuguese boss returned to Chelsea.
"It's a very important day for me, it's my first job," Karanka told reporters. "I think it's the best thing that I can do because I find a club that's like a family with big facilities, a big stadium, big supporters - it's a very important day for me.
"I think it's my time. I have [spent] three years with Mourinho and I think he was supporting me every day. I learned a lot with him and I think I'm ready to start."
Middlesbrough are currently 16th in the Championship table.