Rush was claimed off waivers by the Chiefs on Wednesday, Field Yates of ESPN reports.
Rush (hip) was waived by the Colts on Tuesday.
Rush (shoulder) is practicing Thursday, James Boyd of The Athletic reports.
Rush (shoulder) was not active in Saturday's training camp practice, Joel A. Erickson of The Indianapolis Star reports.
Rush (hamstring) participated in Wednesday's practice, Jake Arthur of SI.com reports.
Rush is dealing with a hamstring injury, Joel Erickson of The Indianapolis Star reports.