The club announced on Wednesday morning the last of the 916 tickets available were snapped up by supporters desperate to see their side in action in this top-of-the-table clash.
Robbie Neilson’s men trail the reigning champions by a point at the cinch Premiership summit.
Saturday’s match will be the first time a top-flight club has had away fans in attendance at Ibrox this season after the lifting of Covid-19 restrictions.
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