Osborn signed a contract with the Patriots on Sunday, Tom Pelissero of NFL Network reports.
Osborn caught two of four targets for nine yards in Sunday's 30-20 loss to the Lions.
Osborn reeled in five of seven targets for 95 yards and one touchdown during Sunday's 30-24 loss to the Lions.
Osborn played 37 of the Vikings' 68 snaps on offense (54 percent) and finished with one catch for three yards on two targets in Saturday's 27-24 overtime loss to the Bengals.
Osborn played 47 of the Vikings' 55 snaps on offense and finished with three catches for 34 yards on four targets in Monday's 12-10 loss to the Bears.
Osborn had one reception for seven yards on two targets in Sunday's loss at Denver.
Vikings head coach Kevin O'Connell said Osborn (concussion) will practice fully Wednesday with the expectation that he'll play Sunday against the Broncos, Andrew Krammer of the Minneapolis Star Tribune reports.
Osborn (concussion) is listed as inactive Sunday versus the Saints.
Osborn (concussion) is listed as questionable but is considered unlikely to play Sunday against the Saints, Ed Werder of ESPN reports.
Osborn has fully cleared the NFL's concussion protocol but remains listed as questionable and isn't considered a lock to play Sunday versus the Saints, Ian Rapoport of NFL Network reports.