The former No. 1 overall pick now will be quarterback Carson Wentz’s blindside protector. The Colts were in search of a starting left tackle after Anthony Castonzo announced his retirement in January.
The Chiefs released Fisher in March in one of their moves to get under the salary cap and revamp their offensive line.
Fisher, who turned 30 in January, missed the Super Bowl after tearing an Achilles tendon in the Chiefs’ AFC Championship Game victory against the Buffalo Bills.
He was selected to his second Pro Bowl last season.
Fisher was selected by the Chiefs with the first overall pick of the 2013 draft. He struggled early in his career, but in recent years began to live up to at least some of the potential the Chiefs saw in him. He has started 113 of the 117 regular-season games he has appeared in during his eight NFL seasons.
ESPN’s Adam Teicher contributed to this report.