The Romanian international will join the team on a free transfer from July 1 after coming to the end of his contract with the Premier League champions.
The 27-year-old told the club's website: "It is a great privilege and honour to join a club like Sunderland. 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 head coach 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."