Japan's Nikkei 225 index rose 1 per cent to 8,870.22. South Korea's Kospi gained 0.8 per cent at 1,964.72 and Australia's S&P ASX 200 added 1 per cent to 4,268.70. Benchmarks in Singapore and New Zealand rose, while shares in the Philippines fell.
Markets in Hong Kong, mainland China and Taiwan remained closed for Chinese New Year.
Japan's powerhouse export sector got a lift from a moderation in the yen's strength even as the country reported its first annual trade deficit since 1980. A strong yen, which hit multiple historic highs last year against the dollar, shrinks the value of overseas earnings when repatriated and makes Japanese products less competitive.
Honda Motor Corp. rose 3.3 per cent. Mitsubishi Motor Corp. jumped 4.4 per cent and Sony Corp. added 3.1 per cent. Tire-maker Bridgestone Corp. added 3.4 per cent.
Technology stocks were elevated after Apple Inc. reported earnings that sailed past analyst estimates. Apple said late Tuesday said it sold 37 million iPhones in the last three months of 2011, vastly exceeding estimates and propelling the company to record quarterly results.
That stellar performance reverberated throughout the global tech industry. South Korea's LG Electronics Inc., which ranks No. 2 globally in flat screen televisions, jumped 4.1 per cent. Hynix Semiconductor Inc., the world's second-largest memory chip maker, added 2.2 per cent.
Stan Shamu of IG Markets in Melbourne said in an email that the gains in Asia suggested "investors are now starting to pay less attention" to Greece, which is struggling to reach a deal with creditors to prevent a chaotic default on its massive debts. A default could trigger a financial crisis in Europe and likely beyond.
Greece is trying to get its creditors to swap Greek government bonds for new ones that have half the face value. Greece faces an important bond repayment deadline in March.
The Dow Jones industrial average closed down 33 points at 12,676 on Tuesday. The Standard & Poor's 500 lost a point to close at 1,315. The Nasdaq added two points to close at 2,787.
Benchmark oil for March delivery rose 35 cents to $99.26 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 63 cents to end at $98.95 per barrel on the Nymex on Tuesday.
In currency trading, the euro rose to $1.3026 from $1.3021 late Tuesday in New York. The dollar rose to 77.91 yen from 77.73 yen.