The Romanian's contract had been due to expire with the Premier League champions at the end of this month, and he will arrive at the Stadium of Light on a four-year deal on July 1.
The 27-year-old has 19 international caps to his name and revealed the vision of head coach Gus Poyet had been a factor in his decision.
"When I left Manchester City it was important that I chose a club with good ambition and a head coach who has the hunger and desire to take the team forward," he told the club's official website.
"After speaking with the boss, I knew this was the right place and he was the right man. I can't wait to start."
Pantilimon made seven league appearances for City last season and is likely to provide stiff competition for current number one Vito Mannone.
"Competition for places is healthy and brings out the best in players," said Sunderland's sporting director Lee Congerton. "We already have a great goalkeeper in Vito Mannone and another one now in Costel.
"Add to this youngster Jordan Pickford, who recently signed a long-term deal and we have a very strong stable of goalkeepers, which is vitally important in the top flight."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
