The bitter boardroom battle, which has gripped the Ibrox club in recent months, took a fresh twist yesterday when news of the resignation was confirmed to the London Stock Exchange.
It was announced Mather had quit by "mutual consent" just six months after he was appointed to the post.
Rangers also confirmed to the London Stock Exchange the departure of non-executive director Bryan Smart.
The shock departures of Mather and Smart leave just two board members at Rangers International - finance director Brian Stockbridge and non-executive director, bus tycoon James Easdale.
In a statement to the London Stock Exchange, the club stressed it was doing everything possible to end the turmoil at Ibrox.
The statement read: "As a matter of priority, the company, working with its advisers, will now seek to strengthen the Board, both to meet the standards required for an AIM company and to achieve stability through a consensus amongst major shareholders, which can then be considered by all shareholders at the Annual General Meeting."
As reported in later editions of yesterday's Evening Times, Mather said he was departing in order to try to restore calm to the club.
On Monday, former director Paul Murray and ex-Rangers International chairman Malcolm Murray were granted an interdict to postpone the meeting.
It came after a dispute over a possible election to determine whether the pair and two others - Alex Wilson and Scott Murdoch - should join the board.
Rangers fans have welcomed the departure of Mather as chief executive.
Supporters' Association general secretary Drew Roberton said: "The fans were unhappy at the way the club was going and the financial performance.
"Fans weren't convinced the current board, including Craig Mather, were the right people to take the club forward."
In a statement, Mather said: "I had real faith in the rebuilding of Rangers and invested significantly in the club. Sadly, those who have been most active in upsetting the very good progress we have been making were not willing to do the same.
"I leave with my head held high and will remain as a shareholder and a supporter of Ally and his team.
"The interests of the club are of paramount importance and I believe these are best served by me leaving the club.
"Despite recent events and speculation, the facts of the matter are that the club is financially secure and in a far better place than it was a year ago."
The boardroom departures of Mather and Smart follow those of non-executive director Ian Hart and chairman Walter Smith.
Former Ibrox manager Smith recently urged the club to resolve its "boardroom turmoil".
Last month, Rangers International returned its first annual results which showed that for the 13-month period until June this year it ran at a operating loss of £14.3million.