Bristol Rovers manager Ray Graydon told the club's website: "He's an excellent defender, good in the air and steady on the ground and I'm pleased that we have added a good, quality, experienced player to our squad."
Edwards has struggled to command a first-team place following the appointment of Paul Hart. He spent time on loan at Oxford (twice), Tranmere, Crystal Palace and Rover's rivals Bristol City during his time at the City Ground.
Nottinghamforest-mad wishes Swanny the very best of luck at his new club.