The 27-year-old's contract at the Recreation Ground was due to expire in 2015, but he has been released early from his deal after Clermont agreed to pay a transfer fee.
Abendanon has made 193 first-team appearances for Bath during his nine years at the club.
"I have loved every minute I have played for Bath and want to thank the club for giving me the opportunities they have," he told the team's official website.
"This has been an extremely hard decision for me, but I feel this is the right time to challenge myself in a new environment.
"I leave behind a set of fantastic fans and a club that I know will be competing for silverware in the coming seasons. I wish everyone at Bath the very best of luck."
Abendanon has won two caps for England at senior international level.