The 225-issue Nikkei Stock Average gained 279.50 points, or 0.96 percent, from Monday to close the day at 29,441.30, marking its highest closing level since May 10.
The broader Topix index of all First Section issues on the Tokyo Stock Exchange, meanwhile, added 15.73 points, or 0.80 percent, to finish at 1,975.48.
Local brokers said the yen's retreat against the U.S. dollar help lift issues whose firms have a broad exposure to overseas markets.
They said that exporters here rely on a weaker yen versus its major counterparts as overseas profits are enhanced when repatriated as is overall competitiveness.
"The weaker yen has strengthened the Nikkei, in addition to growth in high-tech shares," Yutaka Miura, senior technical analyst at Mizuho Securities Co., was quoted as saying.
Other analysts said investors took cues from U.S. shares' performance overnight, particularly technology issues rising as the tech-heavy Nasdaq Composite index closed higher.
"Today's strong market finish is simply a reaction to the gains in the Nasdaq overnight," Jun Morita, general manager of the research department at Chibagin Asset Management, said.
Strategists here also said increased confidence in Japan's vaccination rollout and hence prospects for the full opening up of its economy also helped bolster sentiment.
"Investors have regained confidence in the market as COVID-19 vaccine rollouts have been smooth and accelerated," Morita also said.
Eased concerns about the U.S. Federal Reserve tapering its monetary stimulus in the near term despite signs of inflation also undermined an upbeat market mood, brokers said.
The Fed is set to conclude its two-day policy meeting on Wednesday.
By the close of play, pharmaceutical, metal product and food-oriented issues comprised those that advanced the most by the close of play.
Among tech issues finding favor on their U.S. peers' advance, as well as the yen's softer tone, Screen Holdings gained 1.0 percent, while Tokyo Electron rose 1.7 percent. Taiyo Yuden, meanwhile, ended the day 3.7 percent higher.
Toyota Motor was a notable winner Tuesday, accelerating 1.8 percent to hit a record high.
Drugmakers climbed following U.S. biotech firm Novavax Inc. saying its COVID-19 vaccine is 90 percent effective against the disease and its variants.
Takeda, who will supply the vaccine in Japan, jumped 1.7 percent, while Eisai, the Nikkei's biggest gainer, soared 6.6 percent, following a drug it developed to treat Alzheimer's gaining approval from the U.S. regulators last week.
Issues that rose outpaced those that fell by 1,218 to 841 on the First Section, while 135 ended the day unchanged.
On the main section on Tuesday, 972.79 million shares changed hands, rising from Monday's volume of 854.23 million shares.
The turnover on the second trading day of the week came to 2,372.58 billion yen (21.55 billion U.S. dollars).
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