Mr Zoellick, who was nominated by US President George W Bush, will replace Paul Wolfowitz, who leaves on 30 June.
Mr Wolfowitz is stepping down after two years in office, following a scandal over his role in winning a pay and promotion package for his partner.
A former US deputy secretary of state, Mr Zoellick has most recently worked for investment bank Goldman Sachs.
'Proven track record'
Under an unwritten agreement, the US chooses the head of the World Bank, while European countries select the leader of its sister institution, the International Monetary Fund.
Mr Zoellick's nomination was considered by the World Bank's 24-member board of governors on Monday.
In May, Mr Zoellick acknowledged that he had much work to do to deal with the tensions which unseated his predecessor.
As deputy secretary of state, Mr Zoellick was chief aide to Condoleezza Rice between February 2005 and June last year.
He is also an ex-US trade representative.
The president of the World Bank serves a renewable, five-year term.
"Mr Zoellick brings to the bank presidency strong leadership and managerial qualities as well as a proven track record in international affairs and the drive required to enhance the credibility and effectiveness of the bank," the World Bank board said in a statement.
The executive directors also "affirmed the important role of the bank in addressing poverty and economic growth".