By boosting the continent's resilience to global warming and increasing renewable energy  it hopes the scheme will prevent millions of people from sliding into extreme poverty.
The Africa Climate Business Plan will be presented at COP21, the global climate talks in Paris.
They are aimed at reaching agreement on how to limit global temperature increases to 2 degrees celsius.
"The thing that we wanted to make sure was that Africa wasn't forgotten in the midst of these conversations," Dr Jim Yong Kim, the president of the World Bank told the BBC.
When talks begin, he wants to make sure the conversation is not just about reducing emissions but also about taking steps to cope with the consequences of warming.
And here's why.
The continent emits just 3% of the world's greenhouse gas emissions. Yet even the smallest rise in global temperatures could have far-reaching consequences in sub-Saharan Africa.
Research by the Bank found that without measures to help countries prepare for climate change, 43 million people, mostly in Ethiopia, Nigeria, Tanzania, Angola, and Uganda could fall into extreme poverty by 2030. This will be due to droughts, increasing food prices, and stunting children's growth.
The World Bank is committing a third of the money ($5.7bn) from the International Development Association (IDA), the arm of the World Bank Group that supports the poorest countries.
Looking ahead to climate negotiations in Paris, the World Bank chief acknowledged that reaching a deal won't be simple or easy.
And yet he remained optimistic.
Unlike in 2009, when climate talks in Copenhagen ended in anger and recriminations this time, Dr Kim insisted, would be different: "The resolve of leaders is at an entirely different level to what it was back then.
"There's not a single country in the world that wants to be the stumbling block to getting to an agreement."
And the tricky question of who will pay for any deal? "We think that there is a path to get there."
But if previous climate summits are any guide, Dr Kim's optimism may be sorely tested next week in Paris.
The World Bank wants to raise $16bn to help Africa adapt to climate change.