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The benchmark Nikkei 225 index jumped 162.69 points to 13 169.97, while the Topix index of all first-section shares rose 1.15%, or 12.48 points, to 1 098.88.
A weaker yen and the rise in US shares would help support the Tokyo market, said Hiroichi Nishi, general manager of equities at SMBC Nikko Securities, tipping exporters to lead the session.
"Technical analysis indicates the Nikkei is in a 'buy zone' and cheaper valuations are attracting foreign investors again," Nishi said.
The dollar was at ¥95.40 in Tokyo, against ¥95.37 in New York late Tuesday.
Japan's latest economic data showed the country's trade deficit widened last month as the weak yen pushed up import costs.
But exports jumped 10.1% from the same month a year earlier as the cheaper currency helped make Japanese exporters more competitive overseas.
The data comes as Japanese Prime Minister Shinzo Abe works to stimulate the economy with a big-spending growth plan dubbed "Abenomics".
"This (export data) shows Japanese companies are increasingly in better shape. Their profitability is also rising these days, meaning they are becoming more resilient to potential external shocks," Junko Nishioka, chief economist at RBS Securities Japan, told Dow Jones Newswires.
Naoya Nishimura, strategist at Resona Bank, said: "Even though exporters are being bought back, their rise may be capped as players are also staying on the sidelines ahead of the US Fed's policy decision".
Markets have been speculating about when the Fed, which wraps up a policy meeting later in the day, would start tapering off its $85 billion-a-month bond-buying programme, credited with helping buoy global equities.
The Dow Jones Industrial Average climbed 0.91% to 15 318.23 on Tuesday.
SoftBank's Tokyo-listed shares rose 3.81% to ¥5 440 after a rival bidder for Sprint Nextel dropped its takeover offer.
US satellite television provider Dish Network said it had cancelled plans to submit a revised bid for the US-based wireless carrier.
SoftBank has offered to pay about $21.6bn for the company, in what could be one of the biggest foreign acquisitions by a Japanese firm.
