Tokyo's benchmark Nikkei index today climbed nearly 2% to close at its highest level in more than two years, rising past the psychologically important 20,000 mark.
The Nikkei 225 index rose 1.96%, or 389.88 points, to end at 20,299.38, its highest since August 2015, after a weaker yen lifted exporters.
Analysts said that Japanese share prices rallied as concerns over North Korea, the US economy and a higher yen receded.
Traders were also eyeing the possibility of a snap election, reportedly as soon as next month.
Analysts noted that foreign investors "are sensitive to Japanese politics and have actively traded in times of snap elections.
Japanese shares may slip if Prime Minister Shinzo Abe's "support rate fails to recover (further), which may disappoint foreign investors", they added.
One of the best-performing stocks on the Tokyo market was Nintendo, which jumped more than 7% on strong sales prospects for its Switch games console.
Japanese carmakers were lifted by the weaker yen, with Toyota rising 3.8% and Nissan up 2.1%.
Tokyo was following Wall Street higher, as US stocks logged fresh records in advance of this week's meeting of the Federal Reserve, which is expected to announce a drawdown of its massive bond holdings.
The Fed is due to begin a two-day monetary policy meeting today and markets will be watching to see how chairwoman Janet Yellen describes recent trends in inflation for the world's largest economy, hoping for clues about the timing of the next interest rate rise.