Stewart had an impressive 18-year spell in various boardroom roles at Old Trafford and has also held roles with the FA, Premier League and European Club Association over his long career.
Rangers interim chairman John Gilligan explained the move and the quality Stewart can bring to a side who are once again chasing the title this season.
"Patrick comes with an excellent reputation and background, bringing extensive experience of operating at senior levels during his 20-plus years in football.
"The board continues in discussions with several excellent candidates for the role of chairperson and expect to make an announcement of an appointment in the coming weeks."
Stewart comes into a club who have recently announced a £17m loss for the year to June and are 11 points off league leaders Celtic.
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