Vergini, a centre-back, joins from Estudiantes, having played all but two of their Primera Division Torneo Inicial games this term.
He joins Fiorentina full-back Marcos Alonso in making a temporary switch to the Stadium of Light in January.
Sunderland are also thought to be chasing a deal for Internacional's Argentine playmaker Ignacio Scocco as they march on in the transfer market despite Roberto De Fanti's recent departure from his role as director of football.
The Uruguayan commented: "He's a player I know well because we were following him last season in case we went up with Brighton.
"I watched him for about six months when he was with Newell's Old Boys, and the way he plays, understands football and his physical size made me think of him as a potential signing."
