Butler has signed a two-and-a-half year deal with the West country club after passing a medical on Wednesday.
Butler leaves Albion with a glowing tribute from manager Gary Megson who signed the player in March 2000 for £140,000 from Port Vale.
“If every footballer had Tony’s attitude, management would be a hell of a lot easier,” said the Albin boss.
“He came here to help keep us in Division One, which he did, and played a big part in us reaching the play-offs the following year.
“He then played his part in the squad which won promotion last season, although he probably didn’t play as much football as he would have wanted.
"Tony’s never been an ounce of trouble and is a fantastic pro. I wish him and his family all the best for the future.”
Butler made 81 appearances for Albion and scored one goal.
His last outing for the club came as a substitute in the game with Sheffield Utd at Bramall Lane eight months ago.