The Bears placed Sweeney (undisclosed) on the practice squad/injured reserve Thursday, Brad Biggs of the Chicago Tribune reports.
Sweeney signed with the Bears' practice squad Wednesday, Kevin Fishbain of The Athletic reports.
Sweeney was released by the Bears on Saturday.
The Bears are expected to sign Sweeney to a contract, Jordan Raanan of ESPN.com reports.
The Giants cut Sweeney from their non-football injury list Tuesday, Aaron Wilson of KPRC 2 Houston reports.
The Giants placed Sweeney (undisclosed) on the reserve/non-football illness list Tuesday, per the NFL's transaction log.
Sweeney (undisclosed) was back at the Giants facilities Thursday, Bob Brookover of NJ.com reports.
Sweeney (undisclosed) is under the care of medical professionals in the Giants' training room after experiencing a medical event during Wednesday's practice, Bob Brookover of NJ.com reports. He is stable, alert and conversant.
Sweeney (coach's decision) has been deemed inactive for Saturday's game against the Bears.
Sweeney went without a target while he was on the field for 23 of the Bills' 56 offensive snaps in Sunday's 38-3 win over the Steelers.