Bernanke said the U.S. needs "highly accommodative monetary policy" or low interest rates "for the foreseeable future." That reassured investors who were dismayed by Bernanke's comments last month that the Fed would likely slow its bond purchases later this year and end them around mid-2014 if the economy strengthens. Critics said the Fed bungled its communications strategy.
The Fed has been buying $85 billion of financial assets a month to keep interest rates low and encourage borrowing and spending. That stimulus has driven global stocks higher, so the prospect of reducing it caused market volatility in recent weeks.
"In one short and sweet statement, Federal Reserve chairman Bernanke has flicked a switch on the markets," said strategist Evan Lucas of Australia's IG Markets in a report.
In Europe, Germany's DAX rose 1.2 percent to 8,163.64 and France's CAC-40 gained 0.9 percent to 3,874.19. Britain's FTSE 100 rose 0.8 percent to 6,554.21.
Commodity stocks were the big gainers, as the promise of more support to the U.S. economy, the world's largest, suggested greater demand from consumers and industry. Oil rose to trade briefly above $107 a barrel, near the highest level in more than a year, before easing back down. After soaring $2.99 the day before, it was down $1.15 on Thursday, at $105.37.
Wall Street opened higher, adding to the previous day's gains. The Dow was up 1 percent at 15,437.65 while the broader S&P 500 was 1.1 percent higher at 1,669.73.
A rise in U.S. jobless claims figures by 16,000 to a total of 360,000 failed to move markets much. The level is consistent with steady hiring, though the increase suggests the recovery is still not as fast as hoped.
In Asia, gains were stronger than anywhere else. The Shanghai Composite Index jumped 3.2 percent to 2,072.99, its biggest gain in nearly seven months, while Hong Kong's Hang Seng rose 2.6 percent to 21.437.49. Tokyo's Nikkei 225 added 0.4 percent to 14,472.58.
Markets rebounded from caution a day earlier when unexpectedly weak Chinese trade figures that suggested the world's second-largest economy is slowing more abruptly than forecast.
Elsewhere, Taiwan's Taiex gained 1.8 percent to 8,154.05 and Sydney's S&P/ASX 200 rose 0.8 percent to 4,940.20. Markets in Singapore, Manila and Jakarta also rose.
In currency markets, the dollar stabilized after falling on expectations that the Fed's monetary policy will remain loose for the time being. Looser monetary policy tends to weaken a country's currency.
The dollar was trading at 99.22 yen compared with late Wednesday's 98.83 yen. The euro was down somewhat, at $1.3038 from $1.3140.