The US central bank is widely expected to raise rates for the first time since June 2006 later in the day.
Japan's Nikkei 225 closed 2.61% higher at 19,049.91 in one of its biggest daily gains in more than two months.
Australia's S&P/ASX 200 closed up 2.42% at 5,028.40 after hitting its lowest level since mid-2013 on Tuesday.
The Sydney market was boosted by rises in the banking and commodities sectors.
Sydney-listed shares of BHP Billiton finished the day up 5.6%, while shares of iron ore miner Fortescue Metals and oil and gas producer Santos both added just over 5% each.
Chinese markets headed higher with Hong Kong's Hang Seng index closing up 2% to 21,701.21, and the Shanghai Composite ended 0.2% higher at 3,516.19.
Mainland investors were cautious after a top government think tank - the Chinese Academy of Social Sciences - predicted that the Chinese economy was likely to grow between 6.6% and 6.8% in 2016.
The government's target of about 7% growth this is year is already the slowest pace of expansion in 25 years.
In South Korea, the Kospi index closed up 1.88% at 1,969.4.
Shares in Asia were all in positive territory on Wednesday ahead of the US Federal Reserve's long-awaited interest rate decision.