The 26-year-old defender, capped by Argentina on one occasion, initially moved to the Stadium of Light in January and made 14 appearances in all competitions.
He will now seek to earn a regular place in Gus Poyet's starting XI as Sunderland aim to build on a strong finish to the previous campaign, which ensured they avoid relegation from England's top flight.
"Firstly I'm very thankful to the club for giving me this opportunity. I am very happy to be here once again," Vergini told Sunderland's official website.
"The challenge for me is to become part of this team, and offer all I can so we have a good season.
"The feeling that I've had here at this club has been very good. It’s a big club."
Vergini becomes the sixth close-season addition to Sunderland's squad.
Costel Pantilimon and Jack Rodwell have each come in from Manchester City, while Poyet has also signed Jordi Gomez, Billy Jones and Patrick van Aanholt.
