The Spain international has been without a club since ending his lengthy association with La Liga giants Barcelona at the end of last season.
Valdes was expected to link up with Ligue 1 side Monaco when his deal at Barca ended, but a serious knee injury sustained last March put an end to that move.
The 32-year-old was subsequently linked with a move to United's Premier League rivals Liverpool, before he started training with Louis van Gaal's men in October to finish his rehabilitation.
And United have now confirmed Valdes has penned an 18-month deal at Old Trafford, with an option for a further year.
"It is a real honour to sign for Manchester United. I would like to thank Louis van Gaal and the club for allowing me to do my rehabilitation and to train with the team at the Aon Training Complex," Valdes told United's official website.
"From my short time here I can already see this is a very special club. I worked with Louis van Gaal during my time at FC Barcelona and to have the opportunity to work with him here at Manchester United is a dream come true."
The World Cup winner won the Liga title on six occasions during his time at Barcelona, while he achieved further domestic success in the Copa del Rey on two occasions.
Valdes also enjoyed success with Barca in Europe, winning the UEFA Champions League on three occasions in 2006, 2009 and 2011.
Van Gaal - who gave Valdes his debut at Barca - made it clear that the goalkeeper will be number two behind David de Gea amid speculation the 24-year-old may be sold.
"I am delighted Victor has signed for the club. Victor is a very experienced goalkeeper and his record speaks for itself," the Dutchman added.
"I have said on many occasions that Manchester United will always be interested in the best players.
"Victor has remained very professional throughout his rehabilitation from injury and has been very impressive during his training sessions with the first team over the past weeks.
"He joins the club as the number two goalkeeper and is a great addition to the first team."
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