Tokyo stocks hit their highest level in six months, rising 1.58 per cent or 146.07 points to 9,384.17, Sydney gained 0.33 per cent or 14.0 points to 4,195.9, while Seoul closed 1.30 per cent higher, or 26.02 points, at 2,023.47.
Hong Kong closed up 1.01 per cent to a half-year high, adding 214.34 points to 21,491.62 while Shanghai was flat, ending 0.32 points higher at 2,357.18.
Shares on the Philippine bourse reached a record high, shooting up 2.39 per cent, or 114.14 points, to 4,880.71.
"The US continues to be one of the brighter spots in the global economy," Barclays Capital said in a note, adding that while risks abound, "Greece is less likely to deliver a scare to markets, which already seem to be pricing quite a negative scenario."
Investors were also encouraged by news the European Central Bank plans to swap its Greek debt holdings for new bonds once debt-restructuring negotiations are complete. That moves Athens a step closer to securing a second bail-out package critical to avoiding a messy default on its huge debt.
The news supplied some relief over concern about the eurozone's fiscal woes after the 17-nation bloc told Greece it must accept tough European Union surveillance to unlock the stalled bail-out next week.
Eurozone leaders have for several weeks been negotiating Greece's rescue package of 130 billion euros in fresh loans and a writedown on privately-held government bonds worth 100 billion euros ($131 billion) to avoid defaulting on debt owed on March 20.
Greek lawmakers approved a package of severe austerity measures late Sunday, but Eurogroup chair Jean-Claude Juncker has said that he has not received the "political assurances" from Greece necessary to green light the rescue fund.
The Asian rally was helped by positive signs for the US economy, with the weekly report of new claims for unemployment benefits falling to their lowest level since March 2008 and data on January housing construction confirming a pickup in that depressed sector.
The Dow Jones Industrial Average rose 0.96 per cent to 12,903.71, its highest finish since May 2008, the broad-based S&P 500 added 1.10 per cent and the Nasdaq Composite jumped 1.51 per cent.
General Motors shares rose more than nine per cent despite fourth-quarter earnings missing expectations, with analysts saying they expect a solid year in 2012.
South Korea's Knowledge Economy Minister Hong Suk-woo said Friday that he expects a small trade surplus in February despite difficult economic conditions, Dow Jones Newswires reported.
On currency markets, the euro was at $1.3140 and 103.87 yen, against $1.3135 and 103.60 yen in New York late Thursday.
The dollar bought 79.07 yen, from 78.94 yen.
New York's main oil contract, West Texas Intermediate light sweet crude for March delivery, rose 5 cents to $102.56 per barrel but Brent North Sea crude for April delivery slipped 45 cents to $119.84.
Gold was at $1,730.40 an ounce at 1140 GMT, against $1,728.80 on Thursday.
In other markets:
-- Mumbai was up 135.36 points or 0.75 per cent to 18,289.35 on Friday, its seventh consecutive weekly rise and a fresh six-month high.
Engineering giant Bharat Heavy Electricals Ltd jumped 6.53 per cent to 303.45 rupees while auto and farm equipment maker Mahindra and Mahindra rose 3.29 per cent to 749.3 rupees.
-- Jakarta rose 48.93 points or 1.3 per cent to 3,976.54.
Astra International gained 3.4 per cent to 73,900 rupiah, while Adaro Energy gained 3.1 per cent to 1,980 rupiah.
-- Taiwan rose 0.31 per cent, or 24.66 points, to 7,894.36.
TSMC advanced 1.91 per cent to Tw$80.0 while Acer was 1.01 per cent higher at Tw$44.9.
-- Singapore closed up 0.79 per cent, or 23.39 points, to 3,000.59.
Jardine Cycle and Carriage gained 1.25 per cent to Sg$49.62 and DBS Group advanced 1.75 per cent to Sg$13.94.
-- Kuala Lumpur closed 0.43 per cent higher, or 6.66 points, at 1,557.15.
Plantation giant Sime Darby gained 0.52 per cent to 9.59 ringgit, while telecommunications firm Axiata Group inched up 0.60 per cent to 5.01.
-- Bangkok edged up 0.86 per cent, or 9.68 points, to 1,129.93.
Banpu surged 5.64 per cent to 674.00 baht, while Siam Cement gained 2.02 per cent to 354.00 baht.
-- Wellington edged up 0.1 per cent, or 2.56 points, to 3,289.0.
Fletcher Building closed down 0.92 per cent to NZ$6.43, while Telecom rose 0.94 per cent to NZ$2.145.
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