The Italian had slipped down the pecking order at Old Trafford and was not in Ole Gunnar Solskjaer's plans for the new season.
He has been allowed to return to his homeland after four years in Manchester.
The 29-year-old has penned a five-year deal with the side currently ninth in Serie A after a win and a defeat in two games.
It ends a largely unproductive spell with United since making the move in the summer of 2015 from Torino.
Louis van Gaal brought him in to bolster the full-back ranks with the right-footed player capable of turning out at left-back.
In his first season, he helped them to reach the FA Cup final which they won in extra time after a 2-1 victory over Crystal Palace, and came off the bench in the second half.
His second season saw more limited game time under Jose Mourinho, making 29 appearances in all competitions, but he also helped United to another trophy after they won the Europa League 2-0 against Ajax, starting the match at left-back.
However, the past two years have seen the Italian barely feature for United, due to a combination of injuries and being out favour.
It led to Solskjaer publicly declaring in the summer that he expected him to depart, with younger players being preferred by the Norwegian.
United have had something of a mini exodus in recent days with out of favour stars being shown the door at Old Trafford.
Chris Smalling has departed the club for Roma on a season-long loan deal, having failed to displace Victor Lindelof and big-money signing Harry Maguire.
And, the Alexis Sanchez saga was finally over after completed a season-long loan move to Inter Milan to join up with Romelu Luakau at the San Siro.
Darmian is the latest departure from Old Trafford and could make his Parma debut after the international break when they take on Cagliari at home.