Kunavula, 26, has been allowed to leave his Edinburgh Rugby contract early and departs the Scottish capital having made 23 appearances.
The back-row joined Edinburgh Rugby from Fiji Sevens in 2019 and scored his first try for the club in a then-Guinness PRO14 match against Dragons at the Principality Stadium in March 2021.
Head Coach Mike Blair said: “Mesu is a really talented player but with a number of young Scottish guys in the same position, and with the opportunity for more playing time in Brive, we both agreed it was best for him to move on to further his career.
“We thank Mesu for his hard work and commitment to the club. He’s been a hugely popular figure and moves on with our very best wishes.”
Kunavula added: “I’ve really enjoyed my time at Edinburgh Rugby and I’ve made some friends for life – the boys here are all brilliant and made me feel at home since my first day in Scotland.
“Thank you to all the fans for their support. I’m proud to have represented Edinburgh and I’ll be following the team from afar for the rest of my career.”
