Zoellick, 53, was involved in the launch the Doha round of world trade talks, and later served as deputy secretary of state.
He became the Bush administration's point person 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," the administration official added.
The official 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 his girlfriend Shaha Riza.
The incident increased opposition from many bank staff already unhappy with his leadership.
Henry Paulson, the US treasury secretary and also formerly from Goldman Sachs, led efforts to find Wolfowitz's successor.