Ferdinand, 35, was not offered a new contract by United chiefs but insisted he still felt “fit and healthy, ready for a new challenge and looking forward to whatever the future holds for me”.
The former England centre-back is set to follow defensive partner Nemanja Vidic in leaving the club, with the Serbian having already agreed to join Inter Milan.
Ex-West Ham trainee Ferdinand won six Premier League titles, two League Cups and a Champions League with United after joining from Leeds for £30m, a British record fee at the time, following an impressive 2002 World Cup.
“I have thought long and hard over the last few months about my future and, after 12 fantastic years playing for what I regard as the best club in the world, I have decided the time is right for me to move on,” he added.
“I joined Manchester United in the hope of winning trophies, and never in my wildest dreams could I have imagined how successful we would be during my time here. There have been so many highlights.
“Winning trophies I dreamed about as a kid came true at this great club.”