CEO Craig Mather said he hoped his departure would end the "current hysteria" surrounding the running of the Glasgow club which remains one of the best-supported teams in Britain despite playing in the third tier of the Scottish game.
Rangers, Scottish champions a record 54 times, was forced to relaunch from the fourth tier last year after collapsing under a pile of debt. The demise of such a famous name sent shockwaves through British football where many clubs live beyond their means.
The team won promotion in May but ran up an operating loss of 14 million pounds in the process.
Its untroubled progress through the lower reaches of Scottish football has been accompanied by turmoil off the pitch after Charles Green, an English businessman who led the club's rescue, resigned as CEO in April.
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Mather, who said he had invested a million pounds in the club, stepped in to replace Green initially on an interim basis and was confirmed in the role only three months ago.
Green's departure led to feuding between rival factions seeking to control the club. The club was this week forced to postpone its annual meeting, due to be held next week, after legal action brought by minority shareholders seeking changes to the board.
"My short tenure as chief executive has been beset by incessant attempts to destabilise the operations of the club, all done supposedly in the interests of Rangers," Mather said in a statement on the club website. (http://www.rangers.co.uk)
"I am certain that once the Board is settled Rangers will be restored to the top of Scottish football," he added.
The dispute is being played out publicly because Rangers are listed on London's junior AIM stock exchange.
The club's share price has fallen to 49.7p from a flotation price of 70p last December and its struggles will provide fresh ammunition for critics who say football clubs are inherently risky investments.
(Reporting by Keith Weir; Editing by Neil Maidment and Pravin Char)
