The US president cited a long list of Zoellick's accomplishments, including his willingness "to help struggling nations defeat poverty to grow their economies and offer their people the hope of a better life".
Zoellick's nomination must be approved by the World Bank board of executive directors, representing the lender's 185 member countries.
Zoellick, 53, was involved in the launch the Doha round of world trade talks, and later served as deputy secretary of state.
"Wolfowitz must resign because ... his act of favouritism for personal interest was wrong"
Ibby, Mumbai, India
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He became the Bush administration's point-man on China policy and Darfur, before leaving the government to join investment firm Goldman Sachs last year.
"He has the trust and respect of many officials around the world and believes deeply in the World Bank's mission of tackling poverty," a US administration official added.
He said Zoellick had received "positive reactions" from other countries.
Despite appeals from World Bank member countries and some US politicians to throw the process open to candidates from other countries, Bush stood firm on his wish to appoint an American to the post.
The appointment to the bank's presidency of a consensus individual is crucial, after the furore over Wolfowitz's authorisation of a pay raise for Shaha Riza, a World Bank executive and his domestic partner.
The incident increased opposition from many bank union staff and European governments already unhappy with his leadership. Henry Paulson, the US treasury secretary and also formerly from Goldman Sachs, led efforts to find Wolfowitz's successor.