Kim, Obama's personal nominee, was selected by the World Bank Executive Board as the next president.
He will take over at the beginning of July, after the current president Robert B Zoellick steps down at the end of his five-year term.
Congratulating Kim on his selection, Obama appreciated the strong support offered to him from leaders around the world.
"I am confident that Dr Kim will be an inclusive leader who will bring to the bank a passion for and deep knowledge of development, a commitment to sustained economic growth, and the ability to respond to complex challenges and seize new opportunities," the US President said.
He also expressed satisfaction on the "open" and "transparent" selection process.
Delighted at his selection, Secretary of State Hillary Clinton said Kim "is an excellent selection to lead the World Bank forward, build consensus with donor and borrowing countries, and encourage the increasingly important leadership role of developing countries".
He has demonstrated a deep commitment to solving some of the most pressing challenges we face. For over 25 years, he has worked to fight disease and hunger by pioneering innovative solutions and investing in people and communities, she said.
"We look forward to working with Dr Kim as he shapes an even stronger World Bank. Together, we will help develop economies, build partnerships, and alleviate poverty," Clinton said.