Karanka has been out of work since leaving his job at Middlesbrough in March last year following a four-year spell, which included promotion to the Premier League.
The Spaniard, who previously worked alongside Jose Mourinho at Real Madrid, is now back in English football after agreeing a two-and-a-half-year deal with Forest.
Club chairman Nicholas Randall told the official website: "We are very pleased to have reached terms with Aitor Karanka to become the manager of Nottingham Forest. He is an exceptional candidate who fully subscribes to the vision of the club's owners and Board for the future of the club.
"Our objective is clear; we want to continue building this fantastic football club and lead it to a bright future. The wonderful supporters of the club deserve success and a return to the Premier League. We are all working hard off the pitch to achieve this goal and we believe that Aitor will ensure that we can get the job done on the field of play.
"I want to thank Gary Brazil, his staff and the players for their professionalism and loyalty in the last few days. In particular, the performance against Arsenal was truly outstanding and shows the potential of this fantastic club."
Karanka's first game in charge of Forest, who sit 14th in the Championship table, will be against Aston Villa at home this Saturday.