Boro have been looking for a new boss following Tony Mowbray's exit last month.
Karanka has agreed a two-and-a-half-year contract with Middlesbrough.
"It's a very important day for me," Karanka told a press conference. "It's my first job and the best thing for me because I am joining a club that is like a family with a big facilities, big stadium and big supporters.
"It's my time. I spent three years with Jose Mourinho and he supported me every day. I learned a lot with him and I'm ready to start.
"I have been speaking with him a lot and he recommended to come here because he believes in this project like me."
"Football isn't foreign any more, it's global, we're all one," Middlesbrough chairman Steve Gibson said. "In the past I could rightly be accused of being a 'Little Englander', but we are searching for a first-class coach and where that search takes us can't just be in our back yard, in the north east, England; it has to be global.
"I set down a clear template of what we were looking for and Aitor was the outstanding candidate.
"(Sacking Mowbray) was as tough as you can imagine. I was very fond of Tony, but in this game you are driven by results and the results weren't happening for us. There was an inevitability that we had to change things.
"Having made the decision, over 100 people applied. We had three outstanding candidates and Aitor met the criteria we were looking for."
Karanka worked under Jose Mourinho at Real Madrid.
Mourinho has said: "Karanka was my assistant for three years and I know him very, very well.
"I think whatever club gets him, in England or in another country, will be a lucky club."