The 29-year-old, who skippered the Chiefs to Super Rugby success last season, has agreed a three-year contract with the club.
Connacht chief executive Tom Sears told reporters: "We are absolutely delighted with this key signing - it is a major coup for Connacht.
"This is something we have been working towards for some time now and the fact a player of Craig's calibre has chosen to commit to Connacht is a clear sign of the progress we have made and our intent going forward.
"With a three-year deal Craig has shown he really believes in what we are doing and the potential we have. After leading the Chiefs to the Super XV title last season Craig certainly wasn't short of options - he has chosen Connacht because he wants to be a part of what is happening here."
Clarke will join Connacht at the end of the Super Rugby campaign.