The 31-year-old defender has endured an injury-plagued three seasons since arriving on Wearside, and is set to leave the Stadium of Light upon the expiry of his contract
|33/1||Sunderland are 33/1 with BetVictor to sign Scott Sinclair
However, the 31-year-old has not made a single appearance for the club since Paolo Di Canio took over in March, with reports of disagreements between him and the new boss.
"I’ve had a great three years and would like to thank every #SAFC fan for the support they have shown,” he wrote on Twitter.
"The NE is a special place to play and will always be close to my heart. I wish the club and my teammates all the best for the future."
Bramble, who had been one of the club's top earners, has been linked with a move to MLS.