The Tokyo stock exchange's Nikkei 225 was up 1.4 percent shortly after lunch, while the broader Topix index was up 0.9 percent.
Hong Kong's Hang Seng was at the same time up 1.9 percent, while Shanghai and Shenzhen's composite index stood at plus 0.6 and 1 percent respectively.
South Korea's Kospi index was up 0.6 percent.
At the close on Wall Street on Tuesday evening, the broad S&P 500 index and the Dow Jones industrial index had both risen 1.1 percent. The technology-heavy Nasdaq's composite index had gone up 1.4 percent.
Both the S&P 500 and the Nasdaq's composite index thus noted record-high closing levels.
