The 31-year-old defender said his farewells in a series of messages posted on his Twitter account on Thursday.
Bramble tweeted: "I've had a great three years and would like to thank every #SAFC fan for the support they have shown.
"The NE 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."
The news comes as no surprise with the former Ipswich, Newcastle and Wigan man having played a peripheral part for much of the last campaign after an injury-hit spell on Wearside.