Japan's Nikkei index gained 0.50 percent by lunch, Hong Kong's Hang Seng was up 0.72 percent, Shanghai's Composite climbed 0.23 percent and Sydney's S&P/ASX 200 crept up 0.17 percent despite Australia's flood crisis.
Stocks generally were boosted by Japan's announcement Tuesday that it will buy bonds from a eurozone rescue fund to help finance Ireland's bailout and support the debt-hit bloc, following similar overtures from China.
Finance Minister Yoshihiko Noda said the government would use euro-denominated foreign exchange reserves to buy around 20 percent of a eurozone bond offering this month.
But sentiment remained cautious ahead of Portugal's 2011 debut on the long-term bond market on Wednesday, amid speculation that aggressive intervention by the European Central Bank may help it avoid a bailout.
"Tensions concerning European conditions will continue through the week," Kenichi Hirano, operating officer at Tachibana Securities in Tokyo, told Dow Jones Newswires.
The yen's recent weakness against the euro helped boost stocks in Japanese exporters, with Toyota Motor and Nissan Motor both gaining.
Banking stocks made notable gains in Hong Kong, echoing advances in London, with HSBC up 2.2 percent.
In Shanghai, resource stocks climbed as a weaker dollar helped push up commodity prices.
US stocks posted moderate gains Tuesday, buoyed by a positive start to the quarterly earnings season as aluminium giant Alcoa posted strong figures.
The Dow Jones Industrial Average advanced 0.30 percent, the broader S&P 500 rose 0.37 percent and the tech-rich Nasdaq climbed 0.33 percent.
The euro edged up against the dollar in Asia, fetching $1.3005 in Tokyo morning trade compared with $1.2974 in New York late Tuesday. The euro also rose to 108.23 yen from 108.00 yen. The dollar was flat at 83.23 yen.
Oil prices were mixed, with the closure of two North Sea oil fields compounding supply cuts resulting from the shutdown of an Alaskan pipeline, analysts said.
New York's main contract, light sweet crude for February delivery, rose six cents to $91.17 a barrel. Brent North Sea crude for February delivery dipped seven cents to $97.54.
Gold opened at $1,384.00-$1,385.00 an ounce in Hong Kong, up from Tuesday's close of $1,376.50-$1,377.50.