Japan`s Nikkei 225 closed 2.6 percent higher. South Korea`s Kospi finished with a gain of 1.8 percent.
Hong Kong`s Hang Seng rebounded from a nine-day losing streak to advance 2 percent but gains were less robust on the Shanghai Composite Index in mainland China, which closed 0.2 percent higher. Australia`s S&P/ASX 200 added 2.4 percent.
Investors in Asia won`t learn of the Fed`s decision until they wake up Thursday morning.
European benchmarks were muted in early trading. France`s CAC 40 dipped 0.1 percent while Britain`s FTSE 100 added 0.3 percent. Germany`s DAX was little changed.
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