Carrick fills the vacancy left by Ruben Amorim and takes over from Darren Fletcher, who was placed in temporary charge of first-team duties.
Former players Carrick and Solskjaer were interviewed for the interim role by United's chiefs Omar Berrada and Jason Wilcox, who had been leading the search. Despite Solskjaer's popularity at Old Trafford, United leaned in Carrick's direction, having been impressed with his plans.
Carrick previously managed the club as a caretaker for three games following Solskjaer's dismissal in November 2021, before stepping down for Ralf Rangnick's arrival.
He was appointed the boss of a then-struggling Middlesbrough in October 2022 and guided them to the Championship playoffs in his first season.
However, Boro then missed out on the playoffs in the next two campaigns and Carrick was sacked at the end of the 2024/25 season after 136 games in charge.
Carrick made 464 appearances for United as a player, winning the Premier League title five times.