After agreeing a four-year deal with the Ibrox club, Bougherra will become eligible for the third qualifying round of the Champions League should Rangers overcome FBK next week.
At 6ft 3in, the international team-mate of Brahim Hemdani will command an imposing presence in defence but is equally adept as a holding midfielder.
Meanwhile, Rangers' interest in Cardiff City defender Glenn Loovens appears to have taken a back-seat, although Walter Smith is likely to renew his interest in January when Loovens becomes available on a pre-contract agreement.
