Regional benchmarks opened higher after the central bank lowered its target rate for overnight loans between banks to a range of zero to 0.25 percent and promised to use "all available tools" to heal the U.S. economy.
Many analysts had expected the Fed would cut the rate to 0.5 percent from 1 percent.
In Japan, the Nikkei 225 stock average was down 0.2 percent, or 15.17 points, at 8,552.85 after initially rising 1.1 percent and South Korea's Kospi also gave up early gains to fall 0.3 percent to 1,157.65.
Hong Kong's Hang Seng Index rose 0.7 percent to 15,235.57 while benchmarks in mainland China, Singapore, Thailand and Indonesia added about 1 percent or more. Crude prices gained and the dollar swooned against the euro.
"Every central bank is pumping loads of liquidity into the markets and this is very positive for the markets," said John Mar, co-head of sales trading, Daiwa Securities SMBC Co. in Hong Kong.
Investors also were heartened by Wall Street's reaction to the central bank's announcement. The Dow rose 359.61, or 4.2 percent, to 8,924.14 and the broader Standard & Poor's 500 index advanced 44.61, or 5.1 percent, to 913.18.
Wall Street futures fell modestly, suggesting a lower opening Wednesday in the U.S.
Hong Kong's de facto central bank followed the Fed's move by cutting its base rate by a full percentage point to 0.5 percent. Because the territory's currency is pegged to the dollar, the Hong Kong Monetary Authority's actions usually follow the Fed's.
In currencies, the dollar was little changed at 89.92 yen, and the euro strengthened further to 1.4085.
Oil prices rose, with light, sweet crude for January delivery up 56 cents to $44.16 a barrel in Asian trade. The contract fell 91 cents to settle at $43.60 a barrel overnight.