Following marathon talks, eurozone leaders agreed a deal to keep Greece afloat and remain in the eurozone.
However, the bailout is conditional on Greece passing all the agreed reforms in parliament by Wednesday.
The news lifted stock markets in Europe and the US on Monday, while in Japan on Tuesday the benchmark Nikkei 225 closed up 1.5% at 20,385.33.
Evan Lucas, market strategist at trading firm IG, said that although the deal reduced the risk of a Greek exit from the eurozone right now, the bloc still faced significant issues in the medium term.
"Greek politics could collapse under the strain of this new deal and the subsequent elections that may transpire," he said in a note.
"The viability of the programme is also a large risk if the 'reform' process is disjointed or feeble or straight out rejected by new governments."
Shares of Sony were down 1.2% after the electronics company announced its first new share offering in 26 years.
The move is intended to raise the capital for a larger restructuring programme to push the business towards image sensors and video games.
China bucks trend
Chinese shares headed lower on Tuesday after rallying for the last three sessions to recover losses from its recent plunge.
The Shanghai Composite fell 0.9% to 3,933.25, while Hong Kong's Hang Seng index was down 0.7% at 25,046.75 in afternoon trade.
Shares of telecommunications equipment maker ZTE surged 10% in Shenzhen after its board approved a share buyback plan estimated to be worth 1bn yuan ($161m; £104m).
In Australia, the S&P/ASX 200 index ended up 1.9% to 5,577.40.
Mining heavyweights were among the top gainers with BHP Billiton and Rio Tinto up 2.8% and 3.2% respectively on expectations of good earnings reports next month.
South Korea'S Kospi index finished down at 2,059.23, having risen for the three previous sessions.
Source: BBC