The Australian centre has scored 15 tries in more than 60 appearances for Bath, since joining from the Waratahs in 2009.
However he will now end his three-year association at the club - with Montpellier his most likely destination.
Bath boss Sir Ian McGeechan told the club's official site: "Matt has been a great member of the squad over the last few years, and we will be sad to see him go but understand his decision for doing so.
"We wish him all the best of luck, and I'm sure that he will give his all in helping us make the rest of the season with Bath a success."
Although Carraro has yet to confirm his future plans, he admitted he was sad to be moving on.
"This was a very hard decision to make but the time has come for me to try a new challenge," the 27-year-old said.
"I've hugely enjoyed the last three years here at Bath, have worked with some fantastic people and played in front of some great supporters, all of which I will miss."
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