The benchmark Nikkei 225 index gained 2.13 percent, or 403.06 points, to close at 19,353.24, while the broader Topic index rose 1.59 percent, or 22.26 points, to 1,425.47.
"Tokyo shares are supported by the emergency package... and a weaker yen trading around the high-108 level," Yoshihiro Ito, chief strategist at Okasan Online Securities, said in a commentary.
Japan is unleashing economic stimulus measures worth 108 trillion yen as the country officially declared on Tuesday a month-long state of emergency for Tokyo and six other regions after a spike of coronavirus cases.
Prime Minister Shinzo Abe said that the package was worth 20 percent of GDP, on an "unprecedented scale".
The dollar fetched 108.92 yen in Asian trade, against 108.83 yen in New York.
In Tokyo share trading, Toyota gained 2.03 percent at 6,753 yen after Abe said the automaker was cooperating with other firms to produce ventilators to ease potential hospital shortages.
Uniqlo-chain operator Fast Retailing jumped 7.70 percent to 46,420 yen.
Nintendo was up 0.92 percent to 43,590 yen after a report it has suspended shipments of the Switch game console in Japan as the company was unable to keep up with rising demand due to supply chain disruptions caused by the coronavirus pandemic.
Fujifilm dropped 1.66 percent to 5,732 yen on profit-taking after rallies in recent sessions helped by its anti-flu drug Avigan showing promise as a coronavirus treatment.