Greece, the EU and the IMF agreed early Friday on the final details of a 28 billion euros ($40 billion) savings plan that Athens needs to implement over the next five years in order to obtain cash to pay off its immediate debts.
The European Commission said the deal among international backers on the ground in Athens now has to be "translated into concrete legislative measures" by Greece.
However, investors are still nervous as they wait to see if Prime Minister George Papandreou can get his austerity measures though parliament next week.
Greek lawmakers must pass the bills before June is out, the European Union said.
Tokyo rose 0.85 percent, or 81.87 points, to 9,678.71, Sydney edged up 0.17 percent, or 7.6 points, to 4,508.1 and Seoul climbed 1.70 percent, or 34.95 points, to 2,090.81.
Hong Kong jumped 1.90 percent, or 412.81 points, to 22,171.95 and Shanghai surged 2.16 percent, or 57.96 points, to 2,746.21.
But energy firms were weighed after the IEA said it would release 60 million barrels of crude from its member countries' strategic reserves over the next month, which caused a sharp drop in oil prices.
The agency said it made the move to make up for lost output in Libya and to give the global economy relief from high energy prices. It is only the third time the Paris-based group has taken such a step.
Immediately after the decision New York's main contract, West Texas Intermediate (WTI) for August delivery plummeted $4.39 to close at $91.02 a barrel, a drop of 4.6 percent. Brent North Sea crude for August tumbled $6.95, or 6.0 percent, to $107.26.
In Asian trade the contracts rose, with WTI up $1.13 to $92.15 and Brent $1.28 up at $108.54.
Victor Shum, a Singapore-based analyst with Purvin and Gertz energy consultancy, said: "With lower oil prices, the economy will have a better chance to get stronger. Along with this, the oil demand will also get a boost."
In Tokyo Inpex gained 1.92 percent despite the fall in oil prices, while in Seoul SK Innovation slumped 4.36 percent and Woodside Petroleum dropped 0.5 percent in Sydney.
Regional airlines were boosted by the lower oil prices. In Hong Kong Cathay Pacific rose 5.2 percent and Air China added 7.8 percent while Qantas advanced 1.9 percent in Sydney.
Worries about the global economy were stoked after the US Labor Department reported an unexpected increase in initial jobless claims, by 9,000 to 429,000 in the week to June 18, while the Commerce Department said new-home sales fell 2.1 percent in May.
In Asia, the preliminary HSBC China Manufacturing Purchasing Managers Index hit an 11-month low, reflecting Beijing's efforts to cool the Chinese economy.
And a key indicator of manufacturing in the eurozone plummeted to a 20-month low in June.
Tokyo stayed in positive territory thanks to optimism over the corporate outlook as the recovery from the March 11 quake and tsunami looks to be kicking in.
Nissan said Thursday it expected a 15 percent fall in annual net profit for the year to March 2012 but saw global sales rising 9.9 percent to a record 4.6 million units with full production returning in October.
And Isuzu Motors had on Wednesday issued an aggressive net profit projection for the current fiscal year.
In Hong Kong luxury goods maker Prada ended just 0.25 percent higher on its Hong Kong trading debut as turbulent global markets have sapped sentiment for new offerings.
The European single currency softened to $1.4228 in Tokyo morning trade from $1.4257 in New York late Thursday. It was down to 114.58 yen from 114.72 yen.
The dollar was rangebound at 80.51 yen against 80.52 yen.
Gold closed in Hong Kong at $1,518.50-$1,519.50 an ounce, well down from Thursday's close of $1,544.00-$1,545.00.
In other markets:
-- Taipei fell 0.40 percent, or 34.45 points, to 8,532.83.
Hon Hai was 0.51 percent lower at Tw$97.6 while TSMC fell 0.18 percent to Tw$72.9.
-- Manila surged 1.66 percent, or 70.30 points, to 4,291.44.
Philex Mining was up 9.4 percent at 23.30 pesos and DMCI Holdings added 3.0 percent to 43.20 pesos and Metropolitan Bank fell 0.3 percent to 69.15 pesos.
-- Wellington fell 0.18 percent, or 6.14 points, to 3,455.66.
Contact Energy dragged down the market following a profit downgrade this week.
Contact closed down 1.7 percent at NZ$5.36, while Fletcher Building rose 0.2 percent to NZ$8.67 and Telecom was up 1.2 percent at NZ$2.51.
-- Singapore closed up 22.13 points, or 0.73 percent, to 3,066.85.
Property developer CapitaLand rose 3.55 percent to Sg$2.92 and financial group DBS rose 0.28 percent to Sg$14.40.
-- Jakarta rose 24.9 points, or 0.65 percent, to 3,848.55.
Bank Mandiri rose 0.7 percent to 7,050 rupiah, while car maker Astra International gained 1.6 percent to 61,800 rupiah.
-- Kuala Lumpur ended up 0.09 percent, or 1.47 points, to close at 1,564.66.
Malaysia's largest bank by asset size, Maybank climbed 0.7 percent to 8.88 ringgit while CIMB bank rose 2.0 percent to 8.68 as finance firm RHB Capital shed 3.1 percent to 8.75 ringgit.
-- Bangkok rose 0.87 percent, or 8.81 points, to 1,022.94.
Banpu lost 8.00 baht to 700.00, while PTT gained 5.00 baht to 334.00.
-- Mumbai jumped 2.89 percent, or 513.19 points, to 18,240.68.
India's largest commercial bank State Bank of India rose 6.04 percent or 130.45 rupees to 2,290 while the world's seventh largest steel maker Tata Steel rose 3.9 percent or 21.7 rupees to 578.5.
India's largest software outsourcer TCS closed up 3.88 percent or 42.5 rupees to 1,137.
Copyright AFP (Agence France-Presse), 2011