Valdes parted ways with Barcelona in March 2014 after a cruciate ligament injury ruled him out for the season and the Brazil World Cup.
United handed the goalkeeper a lifeline, allowing him to train with them in October of that year before signing him on an 18-month deal in January 2015.
Valdes, 34, put pen to paper on a two-year deal with the north-west side earlier this month and manager Aitor Karanka called it a 'great coup' for the club.
"You can't imagine how delighted I am because it's not usual to bring players like him to recently promoted teams," Karanka said.
Valdes won the La Liga title on six occassions with Barca and won the 2010 World Cup and 2012 European Championships with Spain.
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