Henson, 32, joined Bath in the summer of 2013 following a spell at London Welsh but has been out injured since November.
The utility back has been part of two grand-slam Six Nations winning teams but a chequered club career has seen him make just as many headlines off the pitch as on it.
After leaving Welsh region Ospreys in 2009 Henson took a sabbatical from rugby to move into showbusiness, before making a comeback with short-lived stints at Saracens and Toulon.
He moved back to Wales with Cardiff but his boozy antics aboard a flight led to his dismissal by the club.
"I've really enjoyed the last couple of seasons here at Bath -- it's a great environment to be part of, and the supporters are fantastic, Henson said in a statement issued by the club.
"I'm looking forward to a new challenge with Bristol, but for the time being my focus is totally on Bath and doing all I can to help finish the season on a high."
Head Coach, Mike Ford, added: "Gavin has brought a lot of experience to the squad in his time here, and his versatility has been a real asset for us. We understand his reasons for joining Bristol, and wish him all the best there."
Bristol, where former England coach Andy Robinson is director of rugby, lead the second-tier Championship as they seek a return to the top-flight.
(Editing by Mitch Phillips)
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