The dollar and euro also picked up against the yen, providing strong support for the Nikkei index as the weakening Japanese currency spurred investors to buy exporter shares.
Tokyo closed up 0.67 percent, or 70.51 points, at 10,578.57 and Sydney ended 0.38 percent higher, adding 17.9 points to 4,708.1.
However, Seoul lost 0.31 percent, or 6.13 points, to close at 1,991.81.
In the afternoon Hong Kong was up 0.27 percent while Shanghai eased 0.24 percent owing to caution ahead of the release of key Chinese economic data later this week.
"There are some concerns that the mediocre performance in the global economy could affect trade and liquidity flows in China," Southwest Securities analyst Zhang Gang told Dow Jones Newswires.
On Thursday and Friday Beijing will release data on key indicators including inflation and trade, with hopes rising that the world's number two economy will show further signs of emerging from its recent slowdown.
Asian markets, which have seen a sell-off in the past few days, bounced following news Tuesday from Alcoa that it saw a profit of $242 million in the three months to December, compared with a year-earlier loss of $191 million.
The company also stayed in the black for the full year, despite aluminium prices falling 12 percent.
"Alcoa's results are generally considered a bellwether for the global economy and the fact that the aluminium giant forecasts higher demand in 2013 appeased investors," noted Stan Shamu, a strategist at IG Market in Melbourne.
However Wall Street ended in negative territory. The Dow fell 0.41 percent, the S&P 500 lost 0.32 percent and the Nasdaq shed 0.23 percent.
With immediate fiscal worries at bay after the United States last week dodged across-the-board tax hikes and automatic spending cuts, dealers are looking for fresh cues to spur buying.
On currency markets the yen weakened as importers and retail investors bought the euro and dollar for overseas purchases.
The dollar bought 87.45 yen in Asian trade, from 86.97 yen in New York late Tuesday.
The euro also bought 114.43 yen from 113.75, while sitting at $1.3085 from $1.3079.
"The yen's resurgence was not something unexpected after falling so much over such a protracted period," Yoshihiro Okumura, general manager at Chibagin Asset Management, told Dow Jones Newswires.
"The market expects that it will resume its weakening trajectory."
And Kuniyuki Hirai, foreign-exchange trading manager at Bank of Tokyo-Mitsubishi UFJ, said: "This is not a market where dollar-selling works. The fact is there are so many who have yet to buy dollars."
Oil prices were lower, with New York's main contract, light sweet crude for delivery in February, dropping 12 cents to $93.03 a barrel while Brent North Sea crude for February lost 14 cents to $111.80.
Gold was at $1,664.95 at 0645 GMT compared with $1,653.49 late Tuesday.
In other markets:
-- Taipei rose 16.98 points, or 0.22 percent, to 7,738.64.
Hon Hai Precision added 0.92 percent to Tw$87.8 while TSMC was 0.3 percent higher at Tw$100.0.
-- Wellington rose 0.32 percent, or 13.17 points, to 4,103.54.
Contact Energy fell 2.3 percent to NZ$5.17 while Telecom was up 3.1 percent at NZ$2.32 and Fletcher Building ended unchanged at NZ$8.45.