The Romania international has agreed a four-year deal with the Black Cats and will join following the expiry of his contract on July 1 after leaving the Premier League champions
The Romanian becomes the Black Cats third summer signing - after Jordi Gomez and Billy Jones - and will compete with Vito Mannone for the No.1 jersey following the expiry of his contract at the Etihad Stadium.
Pantilimon made 18 appearances for City last season - taking advantage of Joe Hart's early term slump in form - but announced his intention to leave the champions after failing to hold on to a regular starting berth.
"It is a great privilege and honour to join a club like Sunderland," he told the club's official website. "They have an amazing history and tradition and of course passionate fans.
"When I left Manchester City it was important that I chose a club with good ambition and a manager who has the hunger and desire to take the team forward.
"After speaking with the boss, I knew this was the right place and he was the right man. I can't wait to start."