The 34-year-old terminated his contract with Inter this month after failing to make an appearance in 2015-16 following back surgery.
The centre-back had been tipped to move to MLS but he has now released a statement via United to confirm that injury problems have forced him to end his playing career.
"The time has come for me to hang up my boots," he said. "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 enjoyed a hugely successful spell at Old Trafford after moving from Spartak Moscow in 2006, winning five Premier League titles, the Champions League and the Club World Cup, and captained the side from 2010 until 2014 after Gary Neville's retirement.
He moved to Inter in 2014 and made 28 appearances in all competitions for the Nerazzurri, all of which came last season.