The former Liverpool defender made his way to Wearside on Monday as a switch from Napoli was completed prior to the transfer deadline.
Dossena spent just 18 months at Anfield during his previous stint in England, but claims to have jumped at the chance to link up with the Black Cats.
The 31-year-old told the club's official website: "It's easy for me to decide to come to Sunderland. I'm very happy to be here, to come to England in the Premier League.
"I'm very happy because I start to work with (an) Italian head coach and I know his kind of football, his kind of work; he worked hard and tried to do his best on the pitch and it's the same from my career.
"The Premier League is the (most) beautiful league in the world. I left in 2010 and now I come back because I think that I can do my best for Sunderland."
Dossena made his bow in English football at the Stadium of Light in August 2008 and is looking forward to taking in a special atmosphere for a second time.
He added: "I want to go out on the pitch in one hour. I hope that I will feature in the Arsenal game.
"My first game for Liverpool was against Sunderland and I remember the fantastic stadium, the atmosphere was very amazing, and now I can see that the club is a great organisation and all the staff try to do the best for my work.
"The fans are very important for (a) player because they are the 12th player on the pitch. When you go in the stadium you can feel the atmosphere, you can feel the support on the team - for me it's important, I want to do my best for the team and for the supporters."