He faced a strong challenge for the post, which has traditionally gone to an American, from Nigerian Finance Minister Ngozi Okonjo-Iweala.
Dr Kim will succeed Robert Zoellick, serving a five-year term beginning on 1 July, the World Bank said in a statement.
Aged 52, Jim Yong Kim is a doctor lauded for his pioneering role in treating HIV/Aids and reducing the impact of tuberculosis in the developing world.
US Treasury Secretary Timothy Geithner said the new president’s background would be valuable in the role.
“His deep development background coupled with his dedication to forging consensus will help breathe new life into the World Bank’s efforts to secure fast economic growth that is widely shared,” Mr Geithner said in a statement.
And outgoing president Mr Zoellick added: “Jim has seen poverty and vulnerability first-hand, through his impressive work in developing countries.
“His rigorous, science-based drive for results will be invaluable for the World Bank Group as it modernises to better serve client countries in overcoming poverty.”
Andrew Mitchell, UK international development secretary and a governor of the World Bank Group, said that “as the first development professional to head the World Bank, Jim Yong Kim’s considerable experience will be vital as he leads it through its ambitious reform and modernisation programme”.
Meanwhile, the bank hailed the selection process as competitive, saying that the challenge posed by Mrs Okonjo-Iweala, as well as by Colombian candidate Jose Antonio Ocampo, would benefit the institution in the long run.
The three candidacies had “enriched the discussion of the role of the president and of the World Bank Group’s future direction”, the World Bank said.
‘New kind of leader’
By convention, the US has always held the top job at the World Bank since it was founded in 1944.
The top job of its sister organisation, the International Monetary Fund, has also always gone to a European but there has been much pressure from emerging economies to open the processes of both organisations to competition.
This year’s vote was the first time the World Bank had to choose between candidates since its creation more than 60 years ago.
Mr Ocampo announced on Friday that he was withdrawing from the race and supporting Ms Okonjo-Iweala.
The World Bank did not provide details of the final vote or which country had backed which candidate.
Dr Kim will oversee a staff of 9,000 economists and development experts, and a loan portfolio that hit $258bn (£163bn) last year.
Mark Weisbrot of the Center for Economic and Policy Research in Washington suggested Dr Kim would make a very different kind of leader.
“There’s just no comparison between him and any of the prior World Bank presidents,” he said.
“The others were political insiders. They spent most of their lives getting rich or becoming politically powerful, or worse. Kim, by contrast, has spent most of his life trying to improve the lives of poor people.”