Ajay Banga has "critical experience mobilizing public-private resources to tackle the most urgent challenges of our time, including climate change," said President Biden's statement.
Banga, 63, is Indian-American and currently serving as vice chairman at equity firm General Atlantic.
He was previously chief executive officer at Mastercard.
His nomination comes amid a push for development lenders to revamp and address global problems like environmental issues more effectively.
US Treasury Secretary Janet Yellen earlier said that lenders' core models, where countries borrow to make specific investments addressing developmental constraints, is "insufficient to meet the moment."
The United States is the World Bank's largest shareholder.
The development lender has just started accepting candidate nominations in a process set to run until March 29, with the bank saying women candidates would be "strongly" encouraged.
The president of the World Bank is typically American, while the head of the International Monetary Fund is customarily European.