The Oakland Raiders released Amerson on Feb. 5, saving some $6 million against their salary cap.
The deal with Kansas City is for one year and $2.25 million in base salary, a source told ESPN's Adam Schefter.
Kansas City also made one subtraction from its secondary when it released veteran cornerback Darrelle Revis earlier this month.
Amerson, 26, played in just six games (all starts) last season and missed the final eight because of a foot injury. He made 33 starts in all for the Raiders in three seasons, intercepting six passes with 46 passes defensed.
After missing two total games in his first three NFL seasons, concussion, shoulder and foot injuries wreaked havoc with his 2017 season.
Amerson, a former second-round pick of the Washington Redskins, was claimed off waivers by the Raiders in 2015. He had signed a four-year extension with Oakland before the 2016 season.
ESPN's Paul Gutierrez contributed to this report.