The 29-year-old had been on the Black Cats' books since 2013 after signing for the Wearsiders from Arsenal.
However, he lost his starting spot to Jordan Pickford last season and made just 13 appearances in all competition.
Mannone, said to have cost the Royals £2m, underwent a medical on Wednesday after agreeing personal terms and a three-year contract.
Reading boss Jaap Stam told the official club website: "We have some outstanding young keepers at the club but, with Ali [Al-Habsi] leaving, we wanted some extra goalkeeping experience to join Anssi [Jaakkola] in the first-team squad.
"Mannone is a great goalkeeper. He has played at the highest level for both Arsenal and Sunderland and he has also played a lot of games in the Championship while on loan with Hull.
"Vito has the abilities we are looking for, he is comfortable playing the ball with his feet and can make the right choices at the right time within our system.
"Of course, he now needs to challenge for a place in the first team, a place that Anssi wants to fight for as well, of course. But we're very glad to have him at the club."