The news, which came amid clashes between protesters and police in Athens, also sent the euro higher but investors remained cautious as Greek MPs must still vote on details of the austerity package on Thursday.
Tokyo closed 0.19 percent, or 18.83 points, higher at 9,816.09, Seoul rose 0.30 percent, or 6.27 points, to 2,100.69 and Sydney added 1.73 percent, or 78.5 points, to 4,608.00.
Hong Kong rose 1.56 percent higher in the afternoon and Shanghai jumped 1.32 percent.
The Greek 'yes' vote to the 28.4 billion euros ($40 billion) in spending cuts unlocks a 12-billion-euro payout from the European Union and the International Monetary Fund.
The cash could help prevent the country defaulting on its huge debts, a situation many fear would spread to other economies and lead to another global financial downturn.
But there was still caution as dealers, who have been closely following events in Greece, now have their eyes on a second vote on the detail behind the measures on Thursday.
The agreement in Athens boosted the euro, which hit a three-week-high of $1.4511 in Tokyo morning trade from $1.4429 in New York late Wednesday. The single European currency was at 116.63 yen from 116.61 yen.
The dollar fell to 80.41 yen from 80.80 yen.
"Although the vote outcome came in line with expectation, the market is confirming risks to the euro stemming from the Greek debt problem are diminishing step by step," said Dai Sato, dealer at Mizuho Corporate Bank.
"Upbeat stock markets are also helping improve risk sentiment, lifting the euro against the dollar," Sato said.
Expectations of a rate hike by the European Central Bank at its policy meeting next week also lifted the euro against the dollar, noted Yuji Saito, foreign exchange market director at Credit Agricole in Tokyo.
US and European stock markets took a cue from the news, with the Dow gaining 0.60 percent, London's FTSE 100 soaring 1.54 percent, Frankfurt's DAX up 1.73 percent the CAC in Paris jumping 1.88 percent.
Oil extended heavy gains made on Wednesday after the vote.
New York's main contract, West Texas Intermediate for delivery in August, climbed 54 cents to $95.31 a barrel in afternoon trade after rising $1.88 on Wednesday.
Brent North Sea crude rose 22 cents to $112.62 after leaping by $3.62 on Wednesday.
However, while world leaders hailed the vote's success as common sense, on the streets of Athens anti-austerity protesters fought with police through the day and late into the night.
An estimated 500 to 600 hardcore demonstrators hurled missiles, according to police, who responded with volleys of tear gas that blanketed Syntagma Square in front of the parliament, while a blaze broke out at the finance ministry.
One demonstrator told AFP: "We're going to carry on the protest until the government falls, and it will fall."
Gold opened at $1,510.00-$1,511.00 an ounce in Hong Kong, up from its Wednesday close of $1,507.00-$1,508.00.
In other markets:
Taipei rose 0.92 percent, or 79.21 points, to 8,652.59.
TSMC rose 1.12 percent to Tw$72.2 while Chunghwa Telecom was up 0.51 percent at Tw$98.8.
Manila gained 0.99 percent, or 41.86 points, to 4,291.21.
San Miguel rose 1.1 percent to 115.20 pesos, Alliance Global Group was up 0.6 percent at 10.94 pesos and SM Investments gained 0.8 percent to 534.50.
But Philippine Long Distance Telephone closed 0.5 percent lower at 2,312 pesos.
Wellington ended 0.98 percent, or 33.43 points, to 3,448.35.
Fletcher Building rose 2.4 percent to NZ$8.62, Telecom added 1.2 percent to NZ$2.455 and Sky City gained 1.7 percent to NZ$3.62.
Copyright AFP (Agence France-Presse), 2011