The American businessman had been named the preferred bidder to buy Rangers by administrator Duff & Phelps last week.
But some Rangers fans greeted the news with anti-Miller banners at last week's game against Dundee United.
And he has now said that "preliminary information" given by the Duff & Phelps was "more optimistic than reality".
"As soon as I was announced as preferred bidder for Rangers, my team began to press ahead with our due diligence," said Miller in a statement.
"Until then, information had been limited to what was made available in the internet data room and questions addressed to the administrators and their staff.
"In addition, I had preliminary discussions with the Scottish footballing authorities and limited discussions with Ally McCoist.
"Upon being named preferred bidder, discussions with Rangers staff started and discussions with all interested parties intensified.
"We continued to work through the holiday weekend in order to meet a very compressed schedule.
"By late Monday night, it became clear to me that preliminary information, discussions and analysis were, unfortunately, more optimistic than reality."
Miller had yet to visit Scotland following his bid for the club but turned in his statement to the reaction from some Rangers fans.
"Having no intention of negatively affecting the potential outcome of the club's future and after hearing the message from Rangers supporters and fans loud and clear ("Yank go home!"), I notified the administrators today that I have withdrawn my bid for Rangers and will not be moving forward," he added.
"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.
"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!"
More to follow.
What does this now mean for Rangers? Will the administrators now accept what was the non-preferred bid (Brian Kennedy's wasn't it?) or will this mean that the 'Gers are edging ever closer to extinction?
I must say I find Miller's worries about the extent of the club's misfortunes rather amusing, surely he along with the rest of us knew the direness of the situation since Valentines Day? I have to give him credit for being magnanamous in defeat, makes me wonder exactly what 'Gers fans problem specifically was with Miller's bid.