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The 29-year-old has signed with the Irish club Connacht for three seasons. He will link up with former Blues coach Pat Lam at the club.
Clarke is the second Chiefs player in a matter of weeks to announce a move after All Black Richard Kahui signalled his departure for Toshiba for Japan.
Lock Clarke has played 57 games for the Chiefs including leading the side to their first Super 15 title last season.
"I was planning on leaving a few years ago but under the new management I was really enjoying it so I decided to stay.
"Then we won the competition, so I wanted to stick around and have a crack at defending the title.
"I've had some great highlights in New Zealand rugby including winning the Investec Super Rugby title and the Ranfurly Shield with Taranaki, but now it's time for my new wife and I to go on a bit of an adventure."
Chiefs' coach Dave Rennie said "Craig's impeccable standards on and off the field have helped raise the bar in this environment.
"He is a passionate Chiefs man and was a massive part of the success we had last season.
His leadership, his work ethic and his attention to detail have continued to impress me.
"We'll miss him, but it's a great opportunity for Craig and Veree and we wish them all the best."
Clarke will not be available for ITM Cup this year for his provincial side Taranaki.
The Chiefs kick off their Super 15 campaign this Friday against the Highlanders in Dunedin.