The benchmark Nikkei 225 index surged 2.66 percent, or 714.12 points, to end at 27,568.15, while the broader Topix index rose 1.74 percent, or 31.14 points, to 1,819.18.

It came after US President Donald Trump signed a $900-billion stimulus bill late Sunday, averting a government shutdown, providing additional payments to unemployed workers and extending an eviction moratorium by a month.

In the US, all three major indices ended at all-time highs, with the Dow Jones Industrial Average up 0.7 percent at 30,403.97.

The broad-based S&P 500 gained 0.9 percent to 3,735.36, while the tech-rich Nasdaq Composite Index advanced 0.7 percent to 12,899.42.

"In the United States, although the virus continues to spread and there's concern over new strains, there is hope for economic recovery thanks to coronavirus vaccines," senior market strategist Yoshihiro Ito of Okasan Online Securities said.

"The Nikkei index continued to grow in the afternoon session and hit a 30-year high," he said. The last time the index reached this level was in August 1990.

After finding several cases of a new COVID-19 variant, which experts fear is more contagious, Japan halted all new non-resident foreign arrivals from overseas until late January.

The number of new infections continues to surge in Japan and Prime Minister Yoshihide Suga has urged people to avoid gatherings, saying "the virus does not take holidays".

The dollar fetched 103.70 yen in Asian trade against 103.76 on Monday in New York.

In Tokyo trading, market heavyweight SoftBank Group soared 4.52 percent to 8,055 yen while Uniqlo casual wear operator Fast Retailing jumped 4.49 percent to 90,810 yen.

The shipping industry was also higher, with Mitsui OSK Lines rising 2.11 percent to 3,145 yen and Kawasaki Kisen Kaisha growing 3.34 percent to 2,070 yen.

Sony was up 2.06 percent to 10,390 yen and Panasonic climbed 2.04 percent to 1,198 yen.