Germany's DAX rose 0.7 percent to 5,612.60 and Britain's FTSE 100 gained 0.4 percent to 5,024.32. France's CAC-40 was up 0.5 percent at 3,726.08.
Many Asian indexes were up as much as 2 percent, while on Wall Street Dow industrials futures were up 11 points at 9,549 and Standard & Poor's 500 futures were up 1.5 points at 1,034.
The Fed's Beige Book released late Wednesday suggested the recession is ending in the U.S. and the economy is finally growing again.
Although economists warn that the recovery is fragile as long as unemployment continues to increase, the Fed's survey showed improvements in economic activity and expectations across most of the country.
"The report sounds like a 'from the ground' confirmation that the recovery is on track. As such, it is consistent with investors taking on more risks and supporting most asset classes," said Sebastien Barbe, analyst at Calyon.
He noted it was still too soon to "claim victory, as retail sales remain flat, labor markets are still weak, and the demand for credit is subdued." But said the report "did nothing to contradict the bulls."
Stronger economic data also emerged in the U.K., where the nation's biggest mortgage lender said house prices rose 0.8 percent in August. Several separate reports have shown a gradual recovery in property markets, which experts say is crucial to consumer confidence.
In Asia, Japan's benchmark Nikkei 225 index rose 201.53 points, or 2 percent, to 10,513.67
Hong Kong's Hang Seng added 218.52, or 1.1 percent, to 21,069.56, Korea's Kospi was up 2.3 percent at 1,644.68 and India's gained 0.6 percent to 16,280.04. Markets in Australia and Taiwan climbed 1.1 percent.
Among major benchmarks, only mainland China's was lackluster, with the Shanghai's index down 0.7 percent.
Tech shares such as Japan's Elpida Memory, up 3.5 percent in Tokyo, were strong after American chip maker Texas Instruments raised its sales forecasts. Meanwhile, Taiwan's Foxconn International Holdings, a major contractor for Apple Inc., jumped 6.5 percent in Hong Kong after the U.S. tech giant's CEO Steve Jobs made a public appearance for first time since his medical leave to announce new products.
Investors showed little reaction to Asia's economic news for the day.
Japan's core machinery orders, a closely watched indicator of corporate capital spending, fell in July after a rise in the previous month, suggesting a patchy recovery in the world's second-largest economy. South Korean and New Zealand central banks, issuing cautious views about their economic prospects, kept their interest rates unchanged as expected.
Overnight in the U.S., the Dow rose 0.5 percent. The index has added 2.9 percent in four days. It was the Dow's second-highest close of the year, just below its Aug. 27 finish of nearly 9,581. The broader Standard & Poor's 500 index gained 0.8 percent to 1,033.37.
Oil prices continued to rise, with benchmark crude for October delivery up 44 cents at $71.75 in European trade after the Organization of Petroleum Exporting Countries decided to keep output levels steady.
OPEC claimed current prices were adequate for both producers and consumers and said it would focus on enforcing existing output quotas among its member countries.
The dollar rose to 92.19 yen from 91.95 yen late Wednesday. The euro fell to $1.4532 from $1.4557 after trading above $1.46 on Wednesday, the highest level since late September 2008.