But gains were limited amid caution ahead of a series of crucial European debt sales this week.
Japan's Nikkei 225 stock average added 0.5 percent to 10,563.33. Banks were among the day's best performers as they tracked gains posted by U.S. financial issues.
Mitsubishi UFJ Financial Group Inc. surged 3.4 percent, and rival Sumitomo Mitsui Financial Group Inc. jumped 2.7 percent.
Elsewhere, Hong Kong's Hang Seng index rose 0.9 percent to 23,962.34,
South Korea's Kospi added 0.2 percent to 2,093.05, and the Shanghai Composite index rose 0.5 percent to 2,818.69.
Australia's S&P/ASX 200 rose 0.2 percent to 4,721.10 as gains among mining companies offset flood-related declines.
Mining giant BHP Billiton Ltd. rose 1.2 percent, while insurers like Insurance Australia Group Ltd. tumbled 3.1 percent.
In New York Tuesday, profits from major retailers and an upgrade to Hewlett-Packard fueled stocks higher. The Dow Jones industrial average rose 34.43 points, or 0.3 percent, to close at 11,671.88.
The broader Standard & Poor's 500 gained 4.73, or 0.4 percent, to 1,274.48. The Nasdaq rose 9, or 0.3 percent, to 2,716.83.
European stock markets had jumped earlier in the day after Japan said it would buy bonds being issued to finance Europe's bailout fund. That would help send bond yields down and ease debt pressures on countries like Ireland and Portugal.
Portugal plans a bond auction of a little over euro1.2 billion ($1.55 billion) Wednesday, followed by bigger issues Thursday from Spain and Italy.
In currencies, the dollar slipped to 83.16 yen from 83.21 yen late Tuesday. The euro stood at $1.3001 from $1.2970.
Benchmark oil for February delivery rose 2 cents to $91.13 a barrel in electronic trading on the New York Mercantile Exchange.
The contract surged $1.86, or more than 2 percent, to settle at $91.11 Tuesday after a presidential panel investigating the Gulf oil spill said the oil industry and the government need to do more to reduce the chances of another large-scale disaster.