He will stand down by 1 February - before the expiry of his term in 2022.
A statement from the bank said the outgoing president would join a firm focusing on infrastructure investments in the developing world and return to the board of a health organisation he founded three decades ago.
"The world of the World Bank Group is more important now than ever as the aspirations of the poor rise all over the world, and problems like climate change, pandemics, starvation and refugees continue to grow in both their scale and complexity", he added.
Announcing his decision on Monday, Kim said in a tweet: "It's been the greatest privilege I could have ever imagined to lead the dedicated staff of this great institution".
The rise of populism and the contentious debate over globalisation is raising the political pressure on leaders of organisations such as the World Bank, he said in an interview.
The 189-nation World Bank is the largest government source for development funding, providing low-priced loans for projects around the world.
Trump's decision could affect how the bank deploys its capital at a time when emerging markets are facing growing stress from rising USA interest rates and trade tensions.
The abrupt resignation could prompt a clash between the Trump administration and other governments over the future of the worldwide body.
Under an unwritten rule, the bank's presidency has always been anointed by its largest shareholder, the United States, an arrangement that also allowed European powers to name the head of the International Monetary Fund. He was born in Seoul and grew up in Iowa.
Former President Barack Obama broke tradition in 2012 by choosing Kim, who was serving as president of Dartmouth College at the time.
The decision ends Kim's six-year tenure and may give US President Donald Trump decisive influence over the future leadership of the global development lender.
The World Bank said Mr Kim had emphasised that infrastructure finance was one of the greatest needs in the developing world and had pushed the bank to work with a new cadre of private sector partners on "sustainable, climate-smart infrastructure".