The Nikkei 225 closed up 50.80 points at 20,650.92, its fifth gain in a row, having risen by 4.4% over the week.
The market was lifted as the yen remained weak against the dollar, which is considered good news for exporters.
In mainland China, stocks rose with the Shanghai Composite climbing 3.5% to 3,957.35.
In Hong Kong, the Hang Seng index closed 1% higher at 25,415.27.
In South Korea, shareholders of construction firm Samsung C&T have approved the merger plans with holding company Cheil Industries.
The deal had been strongly criticised by US hedge fund Elliott Associates, the third-largest shareholder in Samsung C&T.
The share prices of both firms dived after the vote, with Samsung C&T closing down 10.4% and Cheil dropping 7.7%.
The country's benchmark Kospi index closed down 0.5% at 2,076.79.
In Australia, the S&P/ASX 200 index ended flat at 5,670.11.
But Evan Lucas, market strategist with IG, said in a note that he was optimistic about the general outlook for Australian stocks.
"China worries have died down and Greece is now a non-issue (until September, anyway). The next month or two may be the first positive months since February."
Japan's Nikkei index registered its biggest weekly gain since October, while Asian shares were mostly higher as worries over Greece and China eased.