Mr Mather, 42, was appointed Chief Operating Officer and Interim Chief Executive Officer on April 24, 2013 and serves on the Board of Directors.
Walter Smith, Chairman of Rangers, commented: "Throughout his time at the Club, Craig has demonstrated a deep commitment to the Club and has a clear vision of how Rangers should be taken forward.
"He has made an extremely valuable contribution to the Club as Interim Chief Executive Officer and thoroughly deserves the opportunity to lead Rangers as CEO. The Board wish him every success as we all strive to take Rangers back to the pinnacle of Scottish football."
Craig Mather commented: "It is a great privilege to serve as CEO of Rangers. This is a great football club and is recognised as such throughout the UK and internationally.
"I am wholly committed to playing my part in taking the Club back to where it belongs - at the top of Scottish football and competing in Europe. The playing and non-playing staff at Rangers have shown extraordinary dedication in the face of challenging circumstances in recent years and we are united in our belief that great success can be achieved by the Club in future."
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