Russell Martin’s side face the Belgian club in the final qualifying stage after their 4-2 aggregate win over Red Bull Salzburg.
The two-legged tie stands between the Ibrox club and a share of the £40 million prize for league phase qualification.
The first leg is scheduled for next week on either August 19 or 20, with the return leg in Brugge on August 26 or 27.
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Club Brugge entered their match with Salzburg with a 1-0 advantage after an away victory.
However, it was level on aggregate with Salzburg 2-1 up on the night.
Late goals from Carlos Forbs and Hans Vanaken, in the 83rd and 94th minutes respectively, ensured Brugge’s place in the play-off round.
Rangers will now have to overcome the Belgian giants to secure their spot in the UCL.