David Somers was facing one of its major shareholders who has called for the entire board to be removed.
Dave King is seeking shareholder approval at the meeting, due to take place on Friday, to oust the board, with himself, Paul Murray and John Gilligan as replacements.
Somers is the latest director to exit the club after James Easdale quit last week.
Somers said of his short-lived five-month tenure as chairman that it had been a difficult time.
I have worked in the City of London, the world's greatest financial centre for decades and enjoyed considerable success. When I was approached about the chairmanship of Rangers, friends warned me that the world of football has different rules and codes of behaviour.
I now know that is a gross understatement. I am a non-confrontational man and have always tried to bring harmony to boardrooms and with stakeholders.
At the risk of antagonising my army of critics, I would point out that Rangers managed to pay its bills and avoid going under during my tenure. These critics might not agree with how we achieved this.
I look forward to alternative solutions from whoever is running the club in the future.
Despite the personal attacks on me from various sources I genuinely wish the club the very best in the future and I am confident that with such a passionate and vociferous fan base they will be restored to their former glories.
The Rangers board has called on shareholders to vote against King's proposal.