Bramble has signed a three-year deal with the Black Cats after passing a medical.
“Titus was absolutely outstanding for me at Wigan,” Sunderland boss Steve Bruce told the club’s official website.
“He matured into a very, very good player so there was absolutely no hesitation when the chance came to bring him to Sunderland.
“He was certainly the right player at the right price and this is a great deal for the football club.”
