Thornton signed with the Chiefs' practice squad Monday, Ian Rapoport of NFL Network reports.
The Patriots waived Thornton on Saturday, Mike Kadlick of CLNSMedia.com reports.
Thornton is inactive for Sunday's game against the Bears.
Thornton is inactive for Sunday's game against the Titans.
Thornton (ankle) doesn't carry an injury designation for Sunday's game against the Titans.
Thornton (ankle) was limited at practice Thursday.
Thornton caught two of his three targets for 20 yards in Sunday's 25-22 win over the Jets.
Thornton, who has been a healthy scratch the last two games, is in line to be active Sunday against the Jets, Mike Reiss of ESPN.com reports.
Thornton (coach's decision) is inactive for Sunday's game against the Jaguars in London.
Thornton is inactive for Sunday's game against the Texans, Evan Lazar of the Patriots' official site reports.