The new five-year contract will keep the youngster at Ibrox until the summer of 2017.
Wallace has become the fourth Rangers player to sign a new contract with the Scottish outfit this week.
Barrie McKay, Lewis Macleod and Robbie Crawford signed new deals with the club on Tuesday.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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