The S&P 500 closed 0.7 percent higher after Mr Trump’s decsion. Meanwhile, Microsoft shares rose 5.6 percent, which then helped tech-focused Nasdaq soar by 1.5 percent in what the FT reported as a record high.
Japan’s benchmark Topix index rose 1.6 percent, while Australia’s S&P/ASX 200 rose 1.8 percent in early Asia-Pacific trading.
Hong Kong’s Hang Seng rose 0.7 percent and China’s CSI 300 index did not see a huge change.
The S&P 500 is expected to rise 0.1 percent when trading on Wall Street begins today.
And London’s FTSE 100 is expected to fall 0.2 percent.
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5.59am update: Asia stocks rise as positve factory data boosts confidence
Asian shares rose on Tuesday after strong US manufacturing data and gains in tech stocks helped investors look past broader worries about the coronavirus and global economy.
Oil futures gave up their overnight gains and fell in Asia due to nagging worries about an increase in the supply of crude.
US stock futures were 0.02 percent higher in Asia.
An industry gauge released overnight indicated US manufacturing activity expanded in July at the fastest pace in more than a year, which helped Wall Street shares rise on Monday.