The 31-year old only managed 19 appearances for the Black Cats last season having fallen out of favour with new manager Paolo Di Canio, and he has been linked with a move to America.
Bramble's contract expires this summer and he revealed on his personal Twitter account that he will be moving on.
"The NE (North East) is a special place to play and will always be close to my heart. I wish the club and my team-mates all the best for the future," he wrote.
"I've had a great three years and would like to thank every SAFC fan for the support they have shown."