The Argentinian club has confirmed on its official website that they have finally agreed a deal with the Black Cats for the 21-year-old's signature.
Sunderland have also signed young Le Havre midfielder Ba to a three-year contract. He is a France U20 international and made 12 appearances for the French club last season.
Velez say the player and two club officials will head for the Stadium of Light tomorrow in a bid to finalise the transfer.
The news will come as a major boost to manager Paolo Di Canio after it appeared that the proposed deal had stalled earlier this week.
Velez vice-president Julio Baldomar claimed that Peruzzi had rejected the personal terms offered by the Black Cats, although fresh discussions appear to have solved whatever problem there was.
The South American would become the latest addition to a growing list of summer signings at the Stadium of Light which was boosted further last night when United States international striker Jozy Altidore completed his move from Dutch club AZ Alkmaar.
While attacking options have been a major focus for Di Canio, the full-back berths have been high on his wishlist too with left-back Danny Rose having returned to parent club Tottenham after a successful loan spell and Phil Bardsley now seemingly surplus to requirements.
Sunderland missed out on highly-rated Le Havre teenager Benjamin Mendy when he opted to instead join Marseille, but they signed his young team-mate Ba and look to have landed Peruzzi to tick another of the manager's boxes.
They would join Valentin Roberge, Modibo Diakite, Cabral, Altidore, David Moberg Karlsson and Duncan Watmore, and reports in Italy suggest they could also strike a deal for Juventus midfielder Emanuele Giaccherini.