Miller had been named preferred bidder by administrators Duff and Phelps last Thursday over a rival offer from the Blue Knights and Brian Kennedy.
However, the trucking tycoon has now confirmed that he has withdrawn his offer to take over the stricken Glasgow giants.
Miller said in a statement: "By late Monday night, it became clear to me that preliminary information, discussions and analysis were, unfortunately, more optimistic than reality.
"I notified the administrators today that I have withdrawn my bid for Rangers and will not be moving forward.
"I am deeply disappointed as I had considered the opportunity to bid for one of the most historic football clubs in the world, an honour and a privilege.
"I wish Rangers fans, supporters and employees my very best. I hope all your dreams and wishes come true. You certainly deserve it," he added.
"I am most disappointed that I won't have the opportunity to walk into Ibrox Stadium on the day of an Old Firm match as my friends tell me the hair on my arm will stand up and I will never witness such passion and spirit at any sporting event. God Speed, Rangers."
The news will have come as a crushing blow to the club's administrators, with the rival offer from the Blue Knights and Kennedy now seemingly in a one-horse race.
David Whitehouse, joint administrator, said: "We can confirm that Mr Bill Miller has decided not to complete his purchase of Rangers Football Club.
"Since Mr Miller was announced as preferred bidder on Thursday of last week, it is regrettable that more progress could not be made to further the sale of the club.
"We have been informed by his advisors that there were a number of issues with which he felt uncomfortable including legacy contracts, the limitation of potential revenue streams and the expectation of required investment.
"In this case, with time and money for Rangers running out quickly, it was essential to move the process forward with urgency," he added.
"As a consequence of Mr Miller’s bid being accepted, three other bidders have come forward to express their interest in buying the Club and these offers are being evaluated with the utmost urgency.
"There is every opportunity for these bidders to now complete the purchase of the Club prior to the end of the season."