Wolfowitz would replace outgoing World Bank chief James Wolfensohn, who said earlier this month that Wolfowitz was no longer in the running for the top job after a Pentagon official suggested he wanted to stay at the Defence Department.
The US Treasury Department has said it wants a new president in place before Wolfensohn departs in June after 10 years in the post.
By tradition, the United States selects the World Bank president while Europeans nominate a head of the International Monetary Fund.
Bush's choice of Wolfowitz must still be ratified by other World Bank members, a process that could prove unusually contentious.
Target of criticism
Wolfowitz is a deeply controversial figure in Europe because of his role in designing and promoting the Iraq war.
He has also been a frequent target of criticism from congressional Democrats for what they called his "rosy" assessments of the Iraq war. Before the invasion, he assured Congress: "We are dealing with a country that can really finance its own reconstruction and relatively soon."
"We are dealing with a country that can really finance its own reconstruction and relatively soon"
Deputy Defence Secretary
The selection follows Bush's controversial decision to nominate John Bolton, another leading administration hawk, to be US ambassador to the United Nations.
Wolfowitz beat former Hewlett-Packard Co. chief executive Carly Fiorina, who had also been a leading contender for the World Bank presidency.
Wolfensohn, an Australian who became American to take the job, was appointed by president Bill Clinton. But he frequently clashed with Bush's Treasury Department, which decided it was time for a change.