Paul Wolfowitz is to quit as president of the World Bank following a bitter promotion row involving his girlfriend.
Paul Wolfowitz says he has been the victim of a smear campaign
After lengthy talks with the bank's board, Mr Wolfowitz said he would quit the global lending body on 30 June.
He had faced widespread calls for his resignation after being accused of a conflict of interest over a pay rise given to ex-bank employee Shaha Riza.
The White House, which had backed Mr Wolfowitz, said President George W Bush reluctantly accepted his decision.
Mr Bush's former deputy defence secretary joined the World Bank in 2005.
The bank said it would start an immediate search for his successor.
In a statement, the board of directors said it accepted Mr Wolfowitz's assurances that he had "acted ethically and in good faith" in the handling of Ms Riza's role and remuneration.
But it acknowledged that a "number of mistakes" had been made.
In response, Mr Wolfowitz said his decision to resign was "in the best interests" of the institution, which has more than 180 member countries worldwide.
The BBC's Justin Webb in Washington says that by accepting his claim that his actions were honourably intended, the bank has allowed Mr Wolfowitz to leave with, in theory at least, his reputation intact.
He has been under severe pressure for weeks, with a number of European politicians calling on him to step down to prevent the Bank's credibility from being eroded.
The White House strongly supported Mr Wolfowitz - although experts believed its influence would not be enough to save his position in the face of European hostility.
A spokeswoman for the bank's staff association - which had been at the forefront of calls for Mr Wolfowitz's resignation - said: "He has damaged the institution and continues to damage it every day that he remains as its president."
Conflict of interest
Mr Wolfowitz came under fire after details emerged about his role in securing a pay rise for Ms Riza, who used to work at the bank.
When appointed to his post in 2005, he notified the bank of a potential conflict of interest because of his relationship with Ms Riza.
He asked to be allowed to recuse himself, or step aside, from any decisions regarding her future.
The bank's ethics committee acknowledged a conflict of interest but did not allow Mr Wolfowitz to recuse himself.
Paul Wolfowitz's leadership of the World Bank has attracted critics
Mr Wolfowitz then proposed to move Ms Riza to the US state department, where she would be paid and promoted apparently in line with her prospects at the World Bank.
The bank accepted and Ms Riza was duly transferred. Her salary rose quickly to about $193,000 (£98,000) - more than the $186,000 that Secretary of State Condoleezza Rice receives before tax.
A panel of the World Bank later found that Mr Wolfowitz had provoked a "conflict of interest" and broken its code of conduct.
The panel found that the salary Mr Wolfowitz arranged for Ms Riza had been higher than her due and that he had acted "in opposition to the rules of the institution".
While admitting he made a mistake in his handling of the case, Mr Wolfowitz says he has been the victim of a smear campaign and ought to have followed his initial instinct to recuse himself.
The board is made up of representatives of the Bank's leading members including the US, UK, Japan, France and Germany.
The bank gave no further details of its agreement with Mr Wolfowitz.