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Vidic won five Premier League titles and the 2007-08 Champions League in an eight-year spell at Old Trafford, but conceded injuries had forced him to call time on his career.
The Serb was granted his release from Inter Milan earlier this month after an injury-plagued 18-month stint in Italy.
"The time has come for me to hang up my boots," Vidic said in a statement on United's website. "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."
Vidic joined United from Spartak Moscow in January 2006 and formed a formidable centre-back partnership with Rio Ferdinand as United lifted three straight Premier League titles from 2007-09.
He was also part of the United side that beat Chelsea 6-5 on penalties to claim their third European crown in Moscow, with the Red Devils again crowned English champions in 2010-11 and 2012-13.
Vidic left Old Trafford to join Inter in July 2014, playing 28 times for the Serie A side, but after undergoing a hernia operation in August he failed to make a single appearance this season.
