In its annual report on the world economy, the bank said richer countries appeared to be “finally turning a corner” after the financial crisis.
That is expected to support stronger growth in developing economies reports The BBC.
But it warned growth prospects “remained vulnerable” to the impact of the withdrawal of economic stimulus measures in the US.
The US Federal Reserve has already begun to wind down its monthly bond-buying programme, previously set at $85bn (£52bn) a month.
There is concern this could push up global interest rates, which could affect the flow of money in and out of developing countries and lead to more volatile international financial markets.
The World Bank warned that some developing countries “could face crisis risks” if the unwinding of stimulus measures was accompanied by market volatility.
“Growth appears to be strengthening in both high-income and developing countries, but downside risks continue to threaten the global economic recovery,” said World Bank group president Jim Yong Kim.
“The performance of advanced economies is gaining momentum, and this should support stronger growth in developing countries in the months ahead. Still, to accelerate poverty reduction, developing nations will need to adopt structural reforms that promote job creation, strengthen financial systems, and shore up social safety nets.”
The bank forecasts that global GDP will grow by 3.2 per cent this year, up from 2.4 per cent in 2013, with much of the pick-up coming from developed economies.
Developing nations will grow by 5.3 per cent this year, up from 4.8% in 2013.
In an interview with BBC economics correspondent Andrew Walker, World Bank economist Andrew Burns acknowledged that Brazil, Turkey, India and Indonesia were among the countries that could be vulnerable to the impact of US stimulus withdrawal.
However he also noted that the first concrete steps taken by the Federal Reserve to cut back its programme of buying financial assets last month did not severely disturb the markets.