The Tennessee entrepreneur, who was named preferred bidder last week, blamed a combination of grave issues with club finances and "abusive" personal messages of opposition from people claiming to be fans.
Mr Miller's representatives said any buyer would need "deeper pockets" than he has if the club was to be saved.
Stunned supporters' groups fear his departure will lead to a liquidation involving a fire sale of assets such as Ibrox and Murray Park.
Administrators Duff & Phelps claimed there were three other bids on the table – one from the UK, one from the Far East and another from the Middle East.
It is believed neither Sale Sharks owner Brian Kennedy nor the Blue Knights are among the other bidders to have now come forward. One bidder is claimed to have offered close to Mr Miller's £11.2m.
Mr Miller – chairman of Miller Industries, the world's largest manufacturer of towing and recovery equipment – said factors leading to his withdrawal included "preliminary information" given by Duff & Phelps that was "more optimistic than reality".
He also cited the "loud and clear Yank go home" messages from Rangers fans.
Jon Pritchett, chief executive of Club 9 Sports – who had been advising Mr Miller – said fans sent hundreds of "vitriolic expletive-filled emails to the businessman's personal email account, as well as to his son, his company Miller Industries and had even managed to access the email account of his girlfriend.
"The people who reached out were overwhelmingly negative. We know it is not reflective of most fans, but it wasn't a pleasant environment. He's not used to that.
"Being an American, people are suspicious about why you are interested in football. Bearing in mind all the fans have been through, especially what happened with the previous owner, they had a natural distrust and there was an over-reaction, that's understandable.
"People assumed, wrongly, there were ulterior motives with Bill. The assumption is that if they are from the homeland [Scotland] then they have the club's best interests at heart. That's not necessarily the right assumption.
"Bill is a real good guy who would have been a magnificent owner and would have made sure the club was successful."
Mr Pritchett added: "It wasn't until the last three or four days he realised quite how big and how emotional people are over the club, and I think his head overcame his heart a little bit after the weekend and he decided that's it.
"He came to the decision it's a great sports club, which long-term would have great value once it was fixed. But along the way it would probably be expensive and he probably wouldn't be liked. And was it really worth a portion of his children's inheritance on buying a Scottish football club when it is going to be a pain and not enjoyable?
"If someone has the deep pockets and is willing to do the work, I think it could be turned around. It's going to be an expensive process to get fixed. It's not an insignificant amount."
The bid team had already registered a new company, Rangers FC Acquisitions, with Companies House. The incubator firm was to have been used as a vehicle for his rescue of the club while Duff & Phelps aimed to take the original club plc out of administration through a Company Voluntary Arrangement.
But after doing due diligence, Mr Miller found contracts similar to the Ticketus deal, in which future season tickets were sold off to provide immediate income, "robbing the future" and leaving "little cash to operate with".
Ticketus put up more than £20m in exchange for rights to four years of season tickets to help complete Craig Whyte's £1 takeover of Rangers and pay off the club's £18m debt with Lloyds Banking Group.
Concerns also arose that revenues would be lost through the renegotiated player contracts overseen by the administrators, which allows high-value players to walk away from the club on reduced fees.
John MacMillan, general secretary of the Rangers Supporters Association, said: "The club is now in a very precarious position with time getting very short now. And it is a very worrying time. It's looking like that [liquidation] just now. I don't know where else they can turn.
"If Miller felt that a number of supporters were against him, it wouldn't help. But there wasn't enough clarity over his bid anyway."
Mr Miller said: "I wish Rangers fans, supporters and employees my very best. I hope all your dreams and wishes come true. You certainly deserve it.
"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."
Joint administrator David Whitehouse said: "It is regret-table that more progress could not be made to further the sale of the club. As in any company takeover, the selection of a preferred bidder does not guarantee the completion of the sale.
"In this case, with time and money for Rangers running out quickly, it was essential to move the process forward with urgency.
"Mr Miller's bid was deliverable to creditors and was the only deliverable bid on the table at that time. We had no other unconditional bid."