Speaking to Manchester United's official website on Thursday, Michael Carrick said: "My time at this great club will always rank as the best years of my career.
"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.
"I am, and will always be, a Man United fan and will come to as many matches as possible. I would like to wish Ralf Rangnick, 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."
Carrick will be stepping down from his first-team coaching role and leaving the club completely, it was announced after the 3–2 win against Arsenal on Thursday.