Comments from a senior US Federal Reserve official that the case for a rate rise in September had weakened and upbeat durable goods data also boosted sentiment, pushing up the dollar.
Tokyo stocks closed up 1.08 percent, or 197.61 points, to finish at 18,574.44, while Seoul gained 0.73 percent, or 13.91 points, to 1,908 and Sydney rose 1.17 percent, or 60.53 points, to 5,233.30.
Hong Kong rose 1.94 percent in afternoon trading and Shanghai gained 0.81 percent.
Wall Street finished sharply higher on Wednesday, ending a six-day losing streak after fears for China's stalling economy wiped some $8 trillion from global share markets.
Asian shares had ended the day mixed after a volatile session that saw Shanghai veer wildly between losses and gains as dealers weighed news that China's central bank had cut its key rates and moved to free up cash for banks.
Thursday's gains came after William Dudley, the head of the New York branch of the Fed, said the reasons for a rate hike in September had been dampened by the turmoil gripping financial markets.
Dealers had feared that a rise in US rates -- their first in almost a decade -- would heap pressure on the world economy at a time when a slowdown in China is already expected to drag on growth.
A better-than-expected official US manufacturing report showing orders for durable goods -- products expected to last at least three years -- jumped 2.0 percent in July also added to the optimism.
- 'Phenomenal bounce' -
"Strong durable goods numbers out of the US and tempting valuations saw a phenomenal bounce in all US equities," said Angus Nicholson at IG Markets.
"William Dudley's speech seemingly put to bed any prospect of September rate hikes... I think the market will largely be looking towards December as the most likely date if a rate hike happens this year."
In currency markets, the dollar gained and dealers sold the yen -- seen as a safe haven during times of market turmoil -- as risk aversion eased.
In Tokyo trading, the dollar bought 119.97 yen after crossing the 120 yen mark in earlier trading, and was nearly flat against 119.98 yen in New York.
This week it touched a six-month low of 116.18 yen.
The euro was stronger at 136.14 from 135.72 yen. The 19-nation euro fetched $1.1348, up from $1.1312 in US trade.
Gold, also seen as a safe haven when markets are going haywire, traded at $1,127.42, down from $1,131.80 late Wednesday.
Oil rose in Asia as dealers digested a mixed US energy report showing a dip in crude inventories, but barely any decline in production despite sinking prices.
US benchmark West Texas Intermediate for October delivery gained 87 cents to $39.47 while Brent crude for October rose $1.01 to $44.15 in afternoon trade.
In other markets:
-- Taipei rose 1.41 percent, or 108.96 points, to 7,824.55.
Taiwan Semiconductor Manufacturing Co added 1.22 percent to Tw$124.0 while Hon Hai Precision Industry closed 1.32 percent higher at Tw$84.6.
-- Wellington closed up 1.02 percent, or 57.17 points, at 5,634.95.
Spark rose 3.37 percent to NZ$3.225 and Warehouse Group lifted 0.78 percent to NZ$2.60.
-- Bloomberg News contributed to this report --