The Fed also projected a favourable outlook for the U.S. economy at its last policy meeting of the year on Wednesday.
Elsewhere, China said it was in close communication with the United States, while President Donald Trump is expected to meet with top advisers to decide whether to go ahead with planned Dec. 15 tariffs.
Leading gains in the region, the Thai benchmark snapped a 10-day losing streak and rebound from a near one-year closing low hit in the previous session, boosted by energy stocks.
The Malaysian index posted its best intraday percentage gain in over three weeks, boosted mostly by Petronas Gas Bhd, which rose as much as 8.7% and posted its best intraday performance in over six years.
"Rise is on the back of parent Petronas paring down its stake to the domestic institutional funds. This is positive considering the low float of stocks," said Redza Rahman, head of Research at MIDF.
Singapore index ended 0.7% higher, its best intraday gain in nearly three weeks, boosted by gains in bluechip financial stocks.
United Overseas Bank and DBS Group Holdings climbed 1.2% and 1.8%, respectively.
The city state's jobless rate in the third quarter hit a 10-year high and retail sales in October fell 4.3% from year-ago period.
Singapore, which counts the United States and China as key its trading partners, has been extremely reactive to any development on the trade war.
Meanwhile, the Philippine index slipped 0.6%.
The Philippine central bank kept its key policy rate steady for a second straight meeting, in line with a Reuters poll.
Indonesian stocks dropped for the third straight session, after Finance Minister Sri Mulyani Indrawati said the government will not change the legal limit on fiscal deficit.
Index heavyweight Telekomunikasi Indonesia dropped 2.5%.
By Arundhati Dutta
