Over in Australia, the S&P/ASX 200 advanced 1.26%.
MSCI’s broadest index of Asia-Pacific shares outside Japan traded 0.79% higher.
The U.S. Federal Reserve on Wednesday approved a 0.25 percentage point rate hike, the first increase since Dec. 2018.
Officials at the U.S. central bank also signaled an aggressive path ahead, with rate rises coming at the six remaining meetings this year.
Overnight on Wall Street, the Dow Jones Industrial Average climbed 518.76 points, or 1.55%, to 34,063.10 while the S&P 500 advanced 2.24% to 4,357.86. The tech-heavy Nasdaq Composite surged 3.77% to 13,436.55.
The U.S. dollar index, which tracks the greenback against a basket of its peers, was at 98.487 after a recent fall from around the 99 level.
The Japanese yen traded at 118.87 per dollar, weaker than levels below 118 seen against the greenback earlier this week. The Australian dollar changed hands at $0.7288, holding on to gains after yesterday’s jump from below $0.72.
— CNBC’s Jeff Cox contributed to this report.