This will be Carrick's first senior role in management but he took temporary charge of Manchester United for three games after Ole Gunnar Solskjaer was sacked late last year.
The 41-year-old will replace Chris Wilder, who was sacked after a poor start to the season.
Middlesbrough are currently one place above the championship relegation zone.
Carrick initially joined Manchester United as a player from Tottenham Hotspurs in the summer of 2006 and went on to make 464 appearances for the club, winning among others five Premier League titles and the UEFA Champions League in 2008.
"I'm really excited to be here and to be part of a club with such a deep history and tradition," said Carrick.
"Middlesbrough was the first professional club I played for as a nine-year-old boy, so it's a very special feeling to be back here as a head coach.
"Growing up in the north-east myself I'm fully aware of what football means to people. It's a real privilege for me to be in this position and to feel all the passion and enthusiasm you've got for the game and for Boro.
"I'll give everything to help develop the team and keep moving the club forward and make you the supporters proud. I can't wait to get started.”
Middlesbrough chairman Steve Gibson added: "We had identified a number of potentials for the vacancy who we spoke with, and were impressed by all, but Michael was the outstanding candidate."
"Michael has the same values as the club, and we are very much aligned in our ambitions."
Carrick's first game in charge of Middlesbrough will be away at Preston North End on Saturday.
