"This represents an unprecedented opportunity to change the development trajectory of the countries in the region," Kim said.
"With this commitment, we will work with our clients to substantially expand programmes in education, basic health services, clean water and sanitation, agriculture, business climate, infrastructure and institutional reform," he added.
Kim left for Rwanda and Tanzania on Sunday in a show of World Bank support for the entire region.
The new financing from the International Development Association will target 448 projects that are already underway in sub-Saharan Africa.
The region accounts for more than half of the countries eligible for this kind of financing from the IDA, the bank said.