The Nikkei 225 index at the Tokyo Stock Exchange gained 180.88 points to 17,649.40 at the start.
The jump came despite leftist Syriza party winning Greece’s weekend general election.
The choice of Syriza leader Alexis Tsipras as prime minister raised the prospect of tough talks with Greece’s creditors over easing rescue terms, if not more debt restructuring.
Wall Street managed to remain in positive territory on Monday, helped by some positive quarterly earnings.
The Dow Jones Industrial Average edged up 0.03 percent and the broader S&P 500 added 0.26 percent.
European stocks also rose as investors said the markets had largely priced in the result of the Greek election.
The euro has recovered some ground since it fell to around the $1.110 level, the lowest in nearly 12 years, briefly on Monday.
It was at $1.1248 and 133.37 yen early Tuesday, up from $1.1234 and 133.12 yen in New York late Monday.
The dollar edged up to 118.57 yen from 118.49 yen in US trade. (AFP)