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Malpass was approved unanimously by the bank's 25-member executive board on Friday. He will begin a five-year term next Tuesday succeeding Jim Yong Kim, an Obama administration pick who stepped down earlier this year, three years before his term was to end.
Malpass was serving in the Trump administration as Treasury's under secretary of international affairs. He has been a longtime critics of the World Bank and its sister lending organization, the International Monetary Fund.
However in his Treasury post, Malpass helped win support last year for a $13 billion funding increase for the bank.
Malpass, 63, will be the 13th president of the World Bank. Americans have always headed the World Bank, while a European has always headed the IMF since both institutions were created in the mid-1940s.
Critics have said this tradition was no longer valid in a new era with the growing clout of emerging economics such as China. However, no other country put forward a candidate to challenge Malpass.
In a note to World Bank employees after his selection Friday, Malpass said that more than 700 million people remain in extreme poverty in the world. Too many people are not seeing an advance in their living standards, with the poorest nations facing the steepest challenges, he said.
"Faced with these challenges, our twin goals of eliminating extreme poverty and achieving shared prosperity are more relevant than ever," Malpass said. "The Bank Group is strong financially and well equipped with the tools and talent to achieve measurable successes."
Malpass has argued that the World Bank should cut back on its lending to China, which he says is no longer a developing country that depends on the bank's loans because it can borrow on global capital markets. He has argued that the World Bank should be targeting more of its support for development projects to poorer nations.
His candidacy was backed by a global lobbying effort led by Treasury Secretary Steven Mnuchin, who promoted Malpass in discussions with foreign finance officials.
The World Bank board had said last month that it would interview Malpass and expected to make its selection before the World Bank and IMF spring meetings that will be held in Washington next week.