The Italian joins on a two-year deal for an undisclosed fee, ending his eight-year association with Arsenal.
His arrival follows the departure of last season's No.1 Simon Mignolet for Liverpool, a sale which left Keiren Westwood as the club's only senior keeper.
Mannone, 25, made 23 appearances for Arsenal without ever making a first-team place his own and was sent on loan to Barnsley and Hull City during his time in north London.
He said: "Sunderland's potential is incredible. I have come from a big club but, to be honest, I don't see any difference in the facilities. From what I can see on my first day they are brilliant.
"To have good facilities where you can work and improve is something every club wants to achieve. The base is there and I am really happy to be here.
"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 must compete with Westwood for the right to start, and he said: "Of course, every player knows they have competition.
"We live in a world of competition. I will work and do my best to be in the first XI, and then the manager will decide. All I can do is try to show what I am capable of."