Its latest report forecasts global GDP will expand by between 2.9% and 3.3% in 2010 and 2011 - then strengthen to between 3.2% and 3.5% in 2012.
But the report said prolonged rising government debts could push up the price of credit, denting investment and growth in developing countries.
GDP globally contracted by 2.1% in 2009.
Developing economies are forecast to grow between 5.7% and 6.2% each year from 2010 to 2012, according to the report.
High income nations, which saw their economies contract by 3.3% in 2009, are set to grow more slowly this year the report says, at a rate of between 2.1% and 2.3%.
European finance ministers and the International Monetary Fund (IMF) this week moved closer to sealing a 750bn euro (£620bn)stabilisation package that would offer loans to struggling eurozone nations.
It followed a specific programme to help Greece avoid defaulting on its debts.
The World Bank said its predictions were based on the assumption that such efforts by the IMF and European institutions would prevent any country defaulting or requiring a major restructuring of its debts.
However it added that developing countries and regions which relied on trade relations with heavily indebted countries and which were being forced to cut spending in order to trim their deficits may feel "serious ripple effects".
"Demand stimulus in high-income countries is increasingly part of the problem instead of the solution," said Hans Timmer, director of the Prospects Group at the World Bank.
"A more rapid reining in of spending could reduce borrowing costs and boost growth in both high-income and developing countries in the longer run."