The Spaniard was unveiled by chairman Steve Gibson and chief executive Neil Bausor at a press conference at the club's training headquarters on Wednesday morning.
Karanka worked for three years under Mourinho at Real Madrid before leaving the club when the Portuguese departed to rejoin Chelsea in the summer.
And Karanka revealed Mourinho encouraged him to take the job despite Boro's current perilous position just five points clear of the Sky Bet Championship relegation zone.
Karanka said: "I have been three years with Jose Mourinho and he was supporting me every day. I learned from him and his staff and I think I am ready to start.
"You can learn everything from him on the pitch and off the pitch and in the training room, he's great - he's the one.
"He's a person who was supporting me. I was speaking with him and he recommended to me that I should come here because he believes in this project like me."
The former Real Madrid defender had also been pursued by Barclays Premier League strugglers Crystal Palace but was convinced to become Boro's first non-British coach following discussions with Gibson and Bausor this week.
Gibson said: "Football isn't foreign any more, it's global - we're all one.
"In the past I've been accused of being a little Englander but football has become global and we were searching for a first-class coach.
"Where that search takes us can't be in our backyard, can't be in the North East and can't be in England - it's got to be global.
"We set down a clear template of what we were looking for and Aitor was the outstanding candidate."
Bausor said no formal decision had yet been made over the future of the club's backroom staff, including interim coach Mark Venus who is set to leave the club following Karanka's appointment.
"That (the backroom staff) is an ongoing development we are working on and we are not intending to make any comments on that this morning," Bausor said.
"I would like to take the opportunity to thank the interim staff who have been managing the club for the past three weeks, Mark Venus in particular, who have worked tirelessly to get us through the last three games. We would like to place on record our thanks to them."
Source: PA
Source: PA