Robinson was among several key cuts made by the Falcons last week, joining a list that included running back Michael Turner and defensive end John Abraham. The moves freed up about $16 million in salary cap space for Atlanta.
The 30-year-old Robinson signed with Atlanta in 2010 and became a steady figure in the secondary, known especially for his bruising hits. He had four interceptions over the past three seasons.
The agreement with Robinson continued a busy offseason for the Chiefs.
They signed receiver Dwayne Bowe and punter Dustin Colquitt to significant contracts, gave left tackle Branden Albert the franchise tag at more than $9.7 million and have agreed to a trade for quarterback Alex Smith.
Information from The Associated Press was used in this report.