The Serbian centre-back, who started his career at Red Star Belgrade, spent eight years at Old Trafford, winning five Premier League titles, 3 League Cups and the Champions League under Sir Alex Ferguson, but departed for the Italian club in 2014.
Vidic made only 28 appearances for the Serie A side, however, and failed to make a single appearance in 2015-16, with hernia and back injuries leading to his contract being rescinded last week.
The former United captain has now issued a statement confirming his retirement, calling time on a professional career that has spanned 16 years.
In a statement released via the United website, Vidic said: "The time has come for me to hang up my boots. The injuries I have had in the last few years have taken their toll.
"I would like to thank all the players I have played with, all the managers and staff I have worked with, and say a big 'thank you' to the fans for their support over the years."