Vidic, who spent four of his eight years at Old Trafford as club captain, won the 2008 Champions League and five Premier League titles with United as well as three League Cups.
The former Serbia international began his career in his homeland with Red Star Belgrade and also played for Spartak Moscow before moving to United midway through the 2005-06 season. He had been playing for Inter Milan since 2014 but cancelled his contract by mutual consent earlier this month.
Hernia and back injuries meant the former Serbia international failed to feature for Inter this season, but he started 14 games under Roberto Mancini in the 2014-15 campaign.
A statement released to Manchester United's official website read: "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."