On Tuesday Muliaina announced he would be leaving the Chiefs at the end of this year to take up a one-year contract in Ireland.
The 33-year-old fullback has had a season to forget as an elbow injury ruled him out for the rest of the season.
Muliaina will join fellow Chiefs back Aki at the club with Blues prop Tom McCartney after the Super Rugby season.
The Connacht coach, former Blues coach Pat Lam, told the club's website Muliaina had signed a one-year deal as a player-mentor.
"I don't think I need to point out how huge it is to have Mils Muliaina as our first All Black coming to represent Connacht," Lam said. "The second ever All Black and the first ever back to reach 100 test matches is some achievement but what's incredible about Mils is the passion and professionalism he brings whenever he plays and I know he will bring that in the Connacht jersey. At the age of 33, he still has that hunger to play competitive rugby and before his surgery last month he showed his quality and ability to keep playing at the top level in Super Rugby."
Muliaina said he was clear on his role and excited to work with talented young outside backs.