Murray stepped down as chairman in May but stayed on the board, amid speculation of moves to oust him.
He was replaced in the role by ex-Gers boss Walter Smith in what was regarded as a move to bring some stability to the club which re-emerged in the Third Division last year following its descent into administration and then liquidation.
However, in an another day of boardroom shuffles at the Govan club on Tuesday, Murray and fellow non-executive director Phil Cartmell left the board as bus company boss James Easdale’s appointment to the board as a non-executive director was confirmed.
In the open letter, released to Press Association Sport, Murray said: “I make this statement not for self-gratification or sour grapes but because so many fans have told me that dignified silence will be seen as a sign of disrespect.
“My previously criticised silence was observed in the best interests of Rangers.
“I was chairman of this great club for arguably the most difficult year in its long history.
“I was recommended for the role by the investment institutions because of my strong record of honesty, integrity and my successful stewardship, of a 25% shareholding in Manchester United from the bottom to the top but not least because I am a Rangers fan and everything I have done or do is for the club and not self-interest or financial gain.
“It has been a difficult shift and I’d like to thank you, the fans, for your support which I enjoyed as recently as Sunday when I drove over 600 miles to Brora.
“I would also like to thank my wife and daughter for their patience and endurance of great hardship - including no holiday for a year and harassment by journalists in their own garden.
“During the dark days of last summer I put a six-figure sum into the club to literally stop the lights going out at Ibrox at a time when we were in real danger.
“My family have given things up to help save Rangers in this difficult year. There aren’t many wives who would let their husband pay someone else’s significant electricity bill.
“You and I want a squeaky-clean club run by men of the highest integrity and global commercial ability and the highest level of transparency.
“The reason we went down the flotation route was to guarantee transparency, whereas ownership by mysterious individuals does not.
“Events of the last year have seen behaviour that would make the late, great Bill Struth spin in his grave.
“The loss of two men (Phil and myself) with such lengthy financial public company experience and a quality broker will undoubtedly raise questions amongst our institutional shareholders.
“Only time will tell how they will react. These investors and you are our future and you must be listened to and given transparency.
“We cannot go back to the depths of the last two years, we need to hold course. Corporate transparency is the norm and we should embrace it rather than change course when difficult questions are asked.”
The letter continued: “My family and I will always be fans and season ticket holders and I will remain a shareholder and use whatever influence I have to help the Rangers. I want the best for our club both on and off the pitch.
“I want our fans to be talking about football and the development of our rich history and culture. I hope to be the only chairman in our history to preside over a Third Division title!”
Read more on Malcom Murray and Rangers