The Serb, who won five Premier League titles and the Champions League in his eight-year spell at Old Trafford, says injuries have forced his retirement.
Vidic, 34, left Inter Milan by mutual consent in January after failing to make an appearance for the Serie A side this season.
"The time has come for me to hang up my boots," he told  ManUtd.com
"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 Inter Milan on a free transfer in July 2014 and made 28 appearances for the Nerazzurri in his first campaign, but did not feature for Roberto Mancini's side this season following surgery on a hernia in August.
He joined Manchester United from Spartak Moscow in a £7m transfer in January 2006, and quickly formed a centre-back pairing with Rio Ferdinand. Sir Alex Ferguson's side secured a hat-trick of Premier League titles between 2007 and 2009, as well as the 2008 Champions League.
Vidic won two further Premier League titles, in 2010-11 and 2012-13, and three League Cups, but his latter years at Old Trafford were badly affected by injuries, including ruptured cruciate knee ligaments  against Basel in December 2011.
Former Manchester United captain Nemanja Vidic has announced his retirement from professional football.