His departure ends a two-year run at the development bank that was marked by controversy from the start, given his previous role as a major architect of the Iraq war when he served as the No. 2 official at the Pentagon.
"He assured us that he acted ethically and in good faith in what he believed were the best interests of the institution and we accept that," the board said in its announcement of Wolfowitz's resignation.
Wolfowitz was all but forced out, however, by the finding of a special bank panel that he violated conflict-of-interest rules in his handling of the 2005 pay package of bank employee Shaha Riza.
The controversy, which gripped the bank for a month, was seen as a growing liability that threatened to tarnish the poverty-fighting institution's reputation and hobble its ability to persuade countries around the world to contribute billions of dollars to provide financial assistance to poor nations.
By tradition, the World Bank has been run by an American. The Bush administration keenly wanted to keep that decades-old practice firmly intact as the board dealt with Wolfowitz's fate. The United States is the bank's largest shareholder and its biggest financial contributor.
The White House said it would have a new candidate to announce soon, allowing for an orderly transition.
Earlier Thursday, President Bush had seemed resigned to the likelihood that Wolfowitz would lose his job over the conflict-of-interest charges. "I regret that it's come to this," Bush said.
In its statement, the bank's board said it was clear that a number of people had erred in reviewing Riza's pay package.
Wolfowitz, who had fought the pressure to resign for weeks, had sought a recognition from the bank that he did not bear sole responsibility for the matter. In his own statement Thursday, Wolfowitz said he was pleased that the board "accepted my assurance that I acted ethically and in good faith in what I believed were the best interests of the institution, including protecting the rights of a valued staff member."
Now, he said, it was in the best interest of the board that its mission "be carried forward under new leadership."
The board's statement made no mention of any financial arrangements related to Wolfowitz's departure, nor did it speak to Riza's future.
As a result of the controversy, the board pledged to review the World Bank's ethics policies, noting that "the bank's systems did not prove robust to the strain under which they were placed."
Wolfowitz waged a vigorous battle to save his job and maintained he had acted in good faith.
European nations had led the charge for Wolfowitz to resign. Those calls were backed by many on the bank's staff, former bank officials, aid groups and some Democratic politicians.
Until near the end, the Bush administration had professed support for Wolfowitz. But in a shift on Tuesday, the White House indicated for the first time it was open to his departure. It was the same day Wolfowitz made a last-ditch plea to save his job before the board.
Among those mentioned as a possible replacement for Wolfowitz are former Deputy Secretary of State Robert Zoellick, who was Bush's former trade chief; Robert Kimmitt, the No. 2 at the Treasury Department; Treasury Secretary Henry Paulson; former Republican Congressman Jim Leach and Sen. Richard Lugar, R-Ind., and Stanley Fischer, who once worked at the International Monetary Fund and is now with the Bank of Israel.
Paulson, who will work with the president on finding a successor to Wolfowitz, said: "I will consult my colleagues around the world as we search for a leader."
Riza worked for the bank before Wolfowitz took over as president in June 2005. She was moved to the State Department to avoid a conflict of interest but stayed on the bank's payroll. Her salary went from close to $133,000 to $180,000. With subsequent raises, it eventually rose to $193,590. The panel concluded that the salary increase Riza received "at Mr. Wolfowitz's direction was in excess of the range" allowed under bank rules.
Wolfowitz "placed himself in a conflict of interest situation" when he became involved in the terms and details of Riza's assignment and pay package and "he should have withdrawn from any decision-making in the matter," the panel said. Under Wolfowitz's contract as well as the code of conduct for board officials, he was required to avoid any conflict of interest, the report said.
The panel acknowledged that the informal advice Wolfowitz received from the bank's ethics committee "was not a model of clarity."
Still, the entire episode involving Wolfowitz's handling of the pay package "underscores that there is a crisis in the leadership of the bank," the panel said.
Before taking over the bank nearly two years ago, Wolfowitz was the No. 2 official at the Pentagon and played a lead role in mapping the U.S.-led war in Iraq.
Bush tapped Wolfowitz for the job, a move that was approved by the bank's board even though Europeans didn't like him because of his role in the Iraq war.
The 185-nation World Bank, created in 1945 to rebuild Europe after World War II, provides more than $20 billion a year for projects such as building dams and roads, bolstering education and fighting disease. The bank's centerpiece program offers interest-free loans to the poorest countries.
The bank's staff association, which had called for Wolfowitz to step down, said in a statement: "Mr. Wolfowitz has finally done the necessary thing by resigning. He has damaged the institution and continues to damage it every day that he remains as its president."