The 30-year-old South African confirmed his departure from the Recreation Ground on Wednesday. He has been a rumoured target for this season's Heineken Cup semi-finalists and wealthy French club Toulon.
"This has been a very difficult decision for me to make, but one I feel is right," he told the club's official website. "I have loved my time here at Bath. I originally came for two years, and have ended up staying for six."
Claassens has made more than 160 first team appearances for Bath, with just 12 of those outings having been off the replacements' bench.
He added: "I've worked with some fantastic coaches and players, and my wife and I have made many good friends since we moved over, but just feel it is the right time to make a change and have a new challenge."
Bath head coach Gary Gold added: "Mike has been a wonderful player for Bath.
"On and off the field he is the ultimate professional, and his good nature will be missed greatly.
"We completely respect his decision to move on though, and he goes with all our best wishes as he looks to continue his career elsewhere."