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David Malpass, President Trump’s pick to be president of the World Bank and a longtime critic of the influence wielded by the bank and other multilateral institutions, was unanimously approved by its executive board on Friday.

Mr. Trump nominated Mr. Malpass, the Treasury under secretary for international affairs, in February. He will begin his five-year term on Tuesday, the executive directors said in a statement. He succeeds Jim Yong Kim, who stepped down abruptly in January to join an investment firm.

In a note to World Bank employees on Friday, Mr. Malpass, 63, said the organization was capable of “measurable successes” like raising median incomes, improving debt transparency and increasing private-sector development. He urged the bank’s staff to “work tirelessly” toward “a stronger, more stable global economy for all.”

The mission of the bank, which was created in 1944 and is collectively owned by nearly 200 countries, includes reducing global poverty, providing financial aid to needy countries and fighting the effects of climate change. Last year, it provided $20.5 billion for projects involving renewable energy, agriculture and emissions management.

The bank’s priorities are in many way at odds with those of Mr. Trump, a vocal climate change skeptic who has also adopted a tough stance on countering China’s economic prowess, especially in the areas of trade and competition.

Because Mr. Malpass, a former Bear Stearns economist, has questioned World Bank practices like lending money to China, Brazil and other relatively wealthy countries, many people saw his nomination as a sign that Mr. Trump hoped to bend the bank to his views.

But Mr. Malpass has struck a conciliatory tone in recent meetings with dozens of world leaders, an indication that he might not run the bank in lock step with Mr. Trump’s wishes. In an interview with The New York Times last month, he suggested that he was inclined to maintain the spirit of the bank’s existing policies on China and the environment.

Still, Mr. Malpass, who has been deeply involved in the Trump administration’s trade negotiations with China, might seek to scale back the bank’s lending to the country, or at least try to pressure Beijing to be more transparent about the financing of its One Belt, One Road infrastructure initiative.

Steven Mnuchin, the Treasury secretary, said in a statement that Mr. Malpass was an “ideal fit” for his new role. The bank has traditionally been led by an American, although other countries can offer candidates. In this instance, none did.