Perry is set to join the English contingent at Brive
Bristol flanker and captain Joe El Abd, scrum-half Shaun Perry and wing David Lemi will all leave the Memorial Stadium at the end of the season.
The trio are set for their final games for the club at Leicester on Saturday.
BBC Sport understands that El Abd is to join Toulon, while Perry is also heading to France with Brive.
However, Bristol have boosted their ranks with the signings of Gloucester wing Dan Norton, Neath flanker James Merriman and USA Rugby's Robbie Shaw.
Former Connacht and Esher scrum-half Shaw will cover fellow new arrival Jason Spice in the number nine shirt vacated by England international Perry.
"Each player will bring something different and exciting to Bristol Rugby," said head coach Paul Hull.
"James Merriman's speed and ball skills will bring a new dimension to our attack, whilst Robbie Shaw will bring a running threat at scrum-half and no will doubt learn a lot from Jason Spice"
"Dan Norton is a proven talent with great speed and has shown his ability for England Under-20s last season and currently for the England Sevens.
"He now needs an opportunity to play regularly in a team and forge his obvious talent."