The abrupt turnaround will be considered a major embarrassment to the White House but was met with little surprise by political observers. Her nomination caused a revolt in Congress.
Ms Miers met stiff opposition from all sides of the political spectrum and faced mounting criticism about her qualifications.
Democrats accused Mr Bush of bowing to the "radical right wing of the Republican Party".
In a letter to the president she admitted she was concerned that the nomination presented a "burden" to the White House and was not in the best interests of the country.
Mr Bush "reluctantly" accepted the decision in a brief statement.
He said: "It is clear that senators would not be satisfied until they gained access to internal documents concerning advice provided during her tenure at the White House, disclosures that would undermine a President's ability to receive candid counsel."
Ms Miers has never been a judge and had little experience in the appeal courts.
She works as the president's personal lawyer and little was known about her views, most importantly on the landmark Roe vs Wade ruling concerning a woman's right to abortion.
Ms Miers, 60, cited a need to keep internal White House records confidential as the main reason for her withdrawal.
"I have been informed repeatedly that in lieu of records, I would be expected to testify about my service in the White House to demonstrate my experience and judicial philosophy," she wrote.
"While I believe that my lengthy career provides sufficient evidence for consideration of my nomination, I am convinced the efforts to obtain Executive Branch materials and information will continue."
Mr Bush's conservative backers had doubts about her ideological purity, and Democrats had little incentive to help the nominee or the embattled GOP president.
Members of the judicial committee tasked with assessing her nomination had demanded to see the documents which Mr Bush had urged her to keep private.
Senate majority leader Bill Frist said he respected the decision and appreciated Ms Miers' service.
"I look forward with anticipation to the president naming the next nominee quickly," he said.
Mr Bush spent three weeks insisting that he did not want Ms Miers to step down, despite vigorous debate.
The Wall Street Journal had described her selection as "a political blunder of the first order".
The campaign to force her withdrawal had rapidly gathered pace, with conservatives sceptical that she had the credentials to move the nine-member court sufficiently to the right.
Ms Miers's withdrawal means the justice she was chosen to replace, Sandra Day O'Connor, will delay her retirement further, a prospect that concerns many conservatives. O'Connor has been a swing voter on numerous emotional social issues.
The withdrawal stunned Washington on a day when the capital was awaiting potential bad news for the administration on another front the possible indictments of senior White House aides in the CIA leak case.