The bank president has traditionally been an American chosen by the USA administration, but some of the multilateral lender's 189 member countries could mount a new challenge with alternative candidates.
Kim, who served as head of the organization for six years, will join a firm dedicated to raising funds toward infrastructure projects in developing countries.
The World Bank says he will be succeeded February 1 on an interim basis by Cristalina Georgieva, its chief executive officer.
The Trump administration has enjoyed a close working relationship with Kim.
A South-Korean-born physician and anthropologist, raised in the United States, Kim has served as president of the World Bank since 2012.
David Malpass, the Treasury's undersecretary for global affairs, has questioned the need for additional resources for the World Bank and other worldwide financial institutions, arguing instead that the lenders should focus more of their resources on poorer countries and lend less to middle-income countries such as China.
Dr Kim was nominated to the post for two terms by former U.S. president Barack Obama, and advocated financing for green energy projects while dropping support for coal power investments. He was re-elected for a second five-year term that began in 2017.
However, the bank's staff association in 2016 delivered a stinging broadside, citing high levels of disaffection among its 15,000 employees, asserting that it faced a "crisis of leadership" and calling for an end to "back-room deals" over control of the institution.
The reason for Kim's early departure from the role remains unclear.
Internal staff surveys showed rank and file frequently did not trust management or understand the direction in which the institution was headed.