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.