The defender, whose parent club is Estuduantes of Argentina, returns to Wearside having already spent five months at the Stadium of Light during the 2013/14 campaign.
The 26-year old made 14 appearances for the Black Cats following his move in January.
He becomes Sunderland's sixth signing of the summer, following the arrivals of goalkeeper Costel Pantilimon, defenders Billy Jones and Patrick van Aanholt, plus midfielders Jordi Gomez and Jack Rodwell.
Vergini told the club's official website: "I'm very thankful to the club for giving me this opportunity.
"I am very happy to be here once again. I'm also very happy to see so many recognisable faces.
"The challenge for me is to become part of this team and offer all I can so we have a good season.”
Vergini, who has one cap for Argentina, started his career with Paraguayan side Olimpia, then switched to Italian club Verona before moving to Estudiantes in 2013.