He has signed a four-year contract at the Stadium of Light.
The Romanian international goalkeeper represented City on 33 occasions over the past three seasons.
The 27-year old signed from Politehnica Timişoara on a one-year deal in the summer before the 2011/12 season and quickly established himself as a solid presence between the posts, earning himself an extension to his stay at the Etihad Stadium.
Costel played an instrumental role in City’s capture of the Capital One Cup in the 2013/14 season and also appeared seven times for the champions in the Barclays Premier League.
He kept eight clean sheets in the 2013/14 season to aid his team in their ultimately successful pursuit of a league and cup double.
The Bacau-born man made his debut for the club in the League Cup in September 2011 against Birmingham.
In the 2012/13 season, Pantillimon helped the Blues to the FA Cup final, conceding just one goal in the semi-final on City's road to Wembley.
He has been capped for his nation 19 times since making his international debut against Georgia in 2008.
At Sunderland, he is expected to provide Vito Mannone with competition for the no.1 jersey.
Everyone at City would like to wish Costel all the best in his future career and thank him for his valued contribution.