The contract terms for S&P 500 and Nasdaq 100 rose 1.7 percent and 2 percent, respectively, after the verdict, which the Trump administration has also appealed, was made public.
The initial trading in Asia is also characterized by confidence.
The Tokyo Stock Exchange's Nikkei 225 index was up 1.7 percent when traders took a lunch break, while the broader Topix index was up 1.5 percent.
In Hong Kong, the Hang Seng was trading up 0.3 percent at the same time. The Shanghai and Shenzhen composite indices were up 0.7 percent and 1.1 percent, respectively.
Nvidia's quarterly report, which was released after Wall Street closed, has also boosted market sentiment. The American semiconductor giant beat analysts' expectations, and its stock rose nearly 5 percent in after-hours trading.
The court order stops Trump's sweeping 10-percent tariffs on many trading partners, including the EU. The 30-percent tariffs on China and the 25-percent tariffs on certain goods imported from Mexico and Canada are also covered by the decision.
It was still unclear on Thursday morning whether the White House intends to temporarily withdraw the tariffs pending a possible ruling in a higher court.
