The 28-year-old central defender has signed a three-year deal and could make his debut for the Black Cats in tomorrow evening's friendly clash with Hull in Portugal.
Bramble headed out to the Algarve earlier this week after the two clubs settled on an undisclosed fee, understood to be in the region of £1m, and has passed a medical and agreed personal terms, although the final administrative details were only completed today.
Manager Steve Bruce was delighted to have captured a player he first tried to sign 12 months ago after a hugely successful spell together at Wigan.
Bruce said: "Titus was absolutely outstanding for me at Wigan.
"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."