The 24-year-old has left Club Atletico Tigre in his home country for an undisclosed fee and signed a four-year contract with the French club.
Benoit Tremoulinas's departure for Dynamo Kiev left a vacancy at left-back, with the former River Plate player fitting the bill for last season's Coupe de France winners.
Orban's agent Filippo Colasanto had claimed that Sunderland had made a "concrete" offer for his client in June.