The 34-year-old, who joined the club in 2002, has admitted that it has not "sunk in just yet" as he plays his 11th and final season at the club.
"It hasn't quite sunk in just yet, but it will feel odd when I drive out of the car park for the last time. Gloucester Rugby has been a huge part of my life," he told the club's official website.
"My time at Gloucester has been fantastic, I've so much to be grateful for from my time at Kingsholm. There are so many memories and I've made so many good friends. However, I still feel I have a lot of rugby in me and the opportunity at Bristol is an exciting one.
"For the time being though, I'm going to make the most of every moment of my time remaining at Gloucester, and hope that we achieve as much as possible this season."
Buxton skippered Gloucester in the 2007-08 season.