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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.