Carrick’s third and final game as Ole Gunnar Solskjaer’s temporary successor ended with a 3-2 victory over Arsenal, before interim manager Ralf Rangnick takes charge.
The 40-year-old has ended a long association with United which began in 2006 and saw him make 464 appearances, winning five Premier League titles and the Champions League as a player among other honours.
Carrick joined Jose Mourinho’s coaching staff upon his retirement in 2018, then stayed on to serve under Solskjaer as an assistant coach before stepping in to take charge on a caretaker basis upon his departure last month.
The former England international won his first game in charge against Villarreal, securing United’s passage to the Champions League knockout stages, then earned a 1-1 draw away to Premier League leaders Chelsea on Sunday.
“My time at this great club will always rank as the best years of my career,” Carrick said.
“When I first signed over 15 years ago, I never in my wildest dreams could have imagined winning so many trophies and I will certainly never forget the fantastic memories both as a player and as a member of the coaching team.
“However, after a lot of thought and deliberation, I have decided that now is the right time for me to leave the club.
“I want to place on record my thanks to all of the players and a special mention goes to the backroom staff, working long hours with such a great group of people has been a real pleasure and I have made some long-lasting friendships.
“I am, and will always be, a Manchester United fan and will come to as many matches as possible.
“I would like to wish Ralf, the staff, the players and the fans all the best for the future and I look forward to being in the stands and supporting the boys as a fan.”