Green, who owned approximately 8% of the club and was the biggest shareholder, led the consortium that bought the Glasgow club last summer.
A statement was released on the club website and read: "The Company announces that Charles Green has notified the Board that he wishes to step down as chief executive with immediate effect. Recent weeks have seen media interest in the circumstances surrounding the period prior to the acquisition of The Club by the consortium led by Mr Green.
"Whilst Mr Green strenuously denies any wrongdoing, he has recognised that this negative publicity is a distraction and is detracting from the achievements and reputation of The Club. As a result, Mr Green has informed the Board that he will leave his post with immediate effect and leave the Company, following an orderly handover, by the end of May.
"The Board has commenced the search for a new Chief Executive and expects the role to attract high quality candidates from both within and outwith the industry. A further announcement will be made in due course."
Green added: "Recent events have undoubtedly been a distraction for both myself and all involved with Rangers and I feel that it is appropriate that I step down so that The Club can continue to progress back to where it belongs at the pinnacle of Scottish football.
"I am very proud to have been associated with a club of the stature of Rangers and am proud of the achievements of The Club during my tenure as chief executive. My thanks go to the Rangers fans, whose support has been tremendous during my time at The Club."
The club was liquidated, but reformed and joined the fourth tier of Scottish football this term, and have since won the division.
Green's tenure had seen him come under fire - he is the subject of an independent investigation over allegations that he had covert dealings with the previous owner of Rangers, Craig Whyte.
Whyte has threatened legal action, attempting to prove that he still has ownership of Rangers assets.
He has also attracted publicity for alleged racist comments aimed at his fellow director Imran Ahmad.
- Sports & Recreation