Mather is considered part of Green’s group at Ibrox, after he put £1m into the club early on.
A statement to the London Stock Exchange said: “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."
Mather invested in Rangers before its public offering in 2012 and holds 3.1% of the company’s shares in issue..
Mather is also managing director of sports agency Simply Sport Management, and said on his appointment:
"I am delighted to take on the role of chief operating officer of Rangers Football Club and also interim chief executive,"
"This is one of the world's great football clubs with a long and proud history and I had no hesitation in investing personally in Rangers. My own business background is in sport and particularly in youth development, something that will be fundamental to the success of this club.
"Rangers have an important role to play in Scottish football and I think it would be beneficial for this club, and football in general, for me, with other representatives of Rangers, to talk openly and constructively to people in the game and I look forward to doing that."
The appointment follows a rollercoaster year for the football club during which it was booted out of the Scottish Premier League and demoted to the Scottish third division due to financial irregularities. It gained promotion to the second division this season.
Mr Mather pumped £1 million into the "phoenix club" in July last year after the previous Rangers were put into liquidation.