The 33-year-old made 19 appearances for the Seagulls last term after joining on loan in January, helping them finish third, before a play-off semi-final defeat by Sheffield Wednesday.
Sidwell played only four games for Premier League club Stoke last season.
"He knows exactly what the Championship is all about and what it takes to get promoted," manager Chris Hughton said.
"He was excellent for us in the run-in, and was a key figure on and off the pitch as one of the senior members of the squad."
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Championship side Brighton have signed midfielder Steve Sidwell on a one-year deal following his release by Stoke.