Wallace, 52, served as chief financial officer and then chief operating officer at the Abu Dhabi-owned English Premier League club between 2009 and January 2013.
He will seek to bring some stability to Rangers, 54-times national champions who were forced last year to relaunch from the fourth tier of the Scottish game after collapsing under a pile of debt.
His predecessor, Craig Mather, was forced out of the job after only months, undermined by feuding between rival factions seeking to control the club, which is listed on the London AIM stock exchange.
"I am looking forward to meeting the challenges and leading the club to ensure that its off-pitch success matches the performance of the team," Wallace said in a statement.
The Glasgow team has won all 12 league fixtures this season in the Scottish third tier, following on from its promotion at the end of last season.
(Reporting by Keith Weir; editing by James Davey)
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