The 42-year-old is a shareholder and has been the club's director of sports development since October.
He will hold the position until the Third Division outfit appoint a permanent replacement for Charles Green, who resigned as chief executive with immediate effect last week.
A statement to the Stock Exchange confirmed: "Rangers announces that the Board has appointed Craig Mather, aged 42, to the role of Chief Operating Officer for the Group.
In addition, Craig will act as interim Chief Executive Officer and will be a member of the Board as the interim Chief Executive Officer.
"In the meanwhile the search for a permanent replacement for Charles Green will continue and a further announcement will be made as appropriate."
- Board & Management Changes