The positive lead provided a much-needed boost for emerging economies, which have suffered a torrid week as dealers bet on an end to the Fed's monetary easing that has fuelled an investment splurge in Asia.
Tokyo jumped 2.21 percent thanks to a rally in the dollar against the yen, ending 295.38 points higher at 13,660.55. At one point the index was more than three percent higher.
Sydney climbed 0.94 percent, or 47.7 points, to 5,123.4 and Seoul added 1.14 percent, or 21.04 points, to end at 1,870.16.
However, profit-taking sent Hong Kong lower, ending down 0.15 percent, or 31.89 points, at 21,863.51 while Shanghai eased 0.47 percent, shedding 9.66 points to 2,057.46.
In share trading Jakarta ended down 0.04 percent or 1.59 points at 4,169.83, Kuala Lumpur gained 0.04 percent or 0.70 points to 1,721.07 while Bangkok fell 1.01 percent, or 13.68 points, to 1,338.13.
Mumbai rose 1.13 percent, or 206.50 points, to 18,519.44 points, its second straight day of gains, as the rupee showed signs of a recovery.
Meanwhile Manila closed 0.40 percent higher, adding 24.48 points to 6,161.20.
Dealers were given a positive lead from markets in Europe and the United States, which soared on strong data that illustrated a pick-up in economic fortunes.
The preliminary composite purchasing managers index of business activity (PMI) for the eurozone jumped to a 26-month high of 51.7 points for August from 50.5 in July. Anything above 50 indicates expansion, while a reading below 50 points to contraction.
And in the United States the flash PMI came in at 53.9, up from a final July reading of 53.7.
The data followed a similar upturn in China, where HSBC said its PMI reading hit a four-month high of 50.1, which added to recent figures suggesting a slowdown in the Asian economic giant is coming to an end.
On Wall Street the Dow rose 0.44 percent, the S&P 500 added 0.86 percent and the Nasdaq jumped 1.08 percent.
Those rises came despite an unexplained glitch that shut down trading on the Nasdaq for about three hours, which interrupted business on other markets.
Thursday's figures came as some relief to global traders in a week that has seen heavy selling particularly in emerging nations in expectation the Fed's bond-buying scheme known as quantitative easing (QE) will soon come to an end.
Jakarta fell almost nine percent in the four days ending Thursday, while Bangkok was down 6.5 percent over the same period. Manila slid six percent on Thursday after being closed for four days owing to severe flooding and a public holiday.
In forex trade the upbeat sentiment sent the dollar rising to 98.90 yen in late trade, from 98.68 yen late in New York and 98.21 yen in Tokyo Thursday. The euro bought $1.3347 and 132.05 yen compared with $1.3354 and 131.80 yen.
Dealers also took a breather from selling emerging market currencies, with the Indian rupee at 64.07 to the dollar, well up from the record low 65.56 it touched on Thursday. Indonesia's rupiah was at 10,880 from 10,945. Thailand's baht edged up to 31.96 from 32.01.
However, traders remain jittery after the release Wednesday of minutes from the Fed's July meeting was unable to provide clarity on when it may begin to wind down QE.
Expectations of an end to the stimulus have seen foreigners in recent months repatriate some of the vast sums that have poured into emerging economies, in turn hitting currencies and equities.
On oil markets New York's main contract, West Texas Intermediate for delivery in October, was down three cents at $105.00, while Brent North Sea crude for October added five cents to $109.95.
Gold fetched $1,375.62 at 1030 GMT from $1,366.65 late Thursday.
In other markets:
Singapore closed down 0.02 percent, or 0.55 points, at 3,Reuters
Property developer Capital gained 0.65 percent to Sg$3.09 and DBS Bank was up 0.62 percent to Sg$16.16.
Taipei rose 0.75 percent, or 58.93 points, to 7,873.31.
Taiwan Semiconductor Manufacturing Co. added 2.65 percent to Tw$97.0 while Hon Hai fell 0.25 percent to Tw$80.5.
Wellington ended down 0.12 percent, or 5.65 points, at 4,524.21.
Telecom was down 0.67 percent at NZ$2.235 after posting a decline in annual net profit, while Fletcher Building slipped 1.04 percent to NZ$8.60.