The 25-year-old Italian goalkeeper signed a two-year deal with the Black Cats for an undisclosed fee on Wednesday.
"The potential is incredible," Mannone told the club's official website. "I waited a long time for an opportunity like Sunderland, and for me it is a great one.
"I'm very excited. I am here to work hard and to show what I can do."
Mannone leaves Arsenal after seven years at the Emirates Stadium.