The Japanese Nikkei gained 0.31 percent or 29.30 points to 9,380.25, Hong Kong's Hang Seng surged 1.08 percent or 228.54 points to 21,322.75 and the Chinese Shanghai index climbed 1.76 percent, while Indian the benchmark BSE Sensex gained 0.22 percent.
On Tuesday, the Dow Jones Industrial Average gained 0.5 percent to close at its highest level in more than four years after the Institute for Supply Management (ISM) said that U.S. factory activity grew in April at the strongest pace since June.
ISM's manufacturing purchasing managers Index (PMI) improved to 54.8 percent in April from 53.4 percent in March. The data also beats Reuters' expectation for a decline to 53.0 percent.
The effect of the solid U.S. manufacturing activity will be felt in Asia in about six months, supporting my view that Asian exporters will gradually recover towards the end of the year, Hirokazu Yuihama, a senior strategist at Daiwa Securities in Tokyo, told Reuters.
Meanwhile, the news that manufacturing activity in the world's second largest economy improved in April for the fifth straight month also added to the sentiment. The country's Purchasing Managers' Index (PMI) rose to 53.3 in April from 53.1 in March as the nation's economic condition continued to strengthen.
Among the stocks, China Shenhua Energy Co. gained 2.71 percent and China Coal Energy Co. Ltd. surged 3.92 in Shanghai.
In Japan, Toyota Motor Corp. gained 0.47 percent and Honda Motor Co. advanced 0.68 percent, while Sony Corp. rose 0.4 percent.