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.
Shanghai led the charge, closing up 5.34 per cent, or 156.30 points, at 3,083.59, while Hong Kong gained 3.60 per cent, or 758.15 points, to close at 21,838.54.
Tokyo stocks closed up 1.08 per cent, or 197.61 points, to finish at 18,574.44, while Seoul gained 0.73 per cent, or 13.91 points, to 1,908 and Sydney rose 1.17 per cent, or 60.53 points, to 5,233.30.
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.
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The rises 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.
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.
"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 Tokyo trading, the dollar bought 120.21 yen, up from 119.98 yen in New York. This week it touched a six-month low of 116.18 yen.
The euro traded at 135.81 from 135.72 yen, and fetched USD 1.1296, compared to USD 1.1312 in US trade.