According to a report by BBC News, the bank's World Development Report (WDR) urges a rapid scaling-up of spending on clean energy research and protection for poorer countries.
Even a warming of 2 degree Celsius - the G8's target - could reduce GDP in poor nations, the report concludes.
The bank urges governments to conclude an "equitable deal" at December's UN climate summit in Copenhagen.
That "equitable deal" should involve industrialized countries paying for the damage that their historical emissions have caused and will cause in poorer parts of the world, it suggests.
"Developing countries are disproportionately affected by climate change - a crisis that is not of their making and for which they are the least prepared," said World Bank president Robert Zoellick.
"For that reason, an equitable deal in Copenhagen is vitally important," he added.
Part of that deal, according to the report, involves industrialized countries making rapid cuts in their greenhouse gas output, creating "emissions space" to allow for rising fossil fuel use in poorer societies.
The acceptance of "historical responsibility" found resonance among organisations that campaign for the relief of developing world poverty.
"A broad coalition from Bolivian President Evo Morales to the World Bank is united in saying that past emissions matter, and that rich countries have to confront this rather than avoid it," noted Tom Sherman, head of climate change with the charity ActionAid.
The report concludes that policy "cannot be framed as a choice between growth and climate change".
In fact, it says, "climate-smart policies are those that enhance development, reduce vulnerability and finance the transition to low-carbon economic growth".
The bank notes that some developing countries' outlay on coping with weather emergencies is already rising.
Poor countries in Africa and Asia could see their GDP fall by about 5 percent under a global warming of 2C.
"Grappling with climate shocks that are already hampering development will not be easy," said Rosina Bierbaum, co-director of the WDR and dean of the University of Michigan's School of Natural Resources and Environment.
"But promising new energy technologies can vastly reduce future greenhouse gas emissions and prevent catastrophic climate change," she added.