MSCI's broadest index of Asia-Pacific shares outside Japan added 0.3 percent. Japan's Nikkei jumped 1.1 percent, while S&P 500 e-mini futures edged up 0.1 percent, after Wall Street posted solid gains overnight.
In its statement issued after its meeting on Wednesday, the Fed left interest rates unchanged on Wednesday, but kept the door open to a hike in June while showing little sign it was in a hurry to tighten.
"The committee continues to closely monitor inflation indicators and global economic and financial developments," the Fed said following its two-day meeting.
The BOJ's policy decision, which is often announced around noon in Tokyo, or 0300 GMT, will be a close call.
Policymakers are likely hesitant to take further steps after unveiling their negative interest rate policy in January, though a strong yen and receding inflation expectations could prompt them to ease further.
Data issued early on Thursday showed Japan's core consumer price index fell 0.3 percent from the year-ago period, compared with economists' median estimate for a 0.2 percent gain.
Separate data showed industrial output rose more than expected and labour demand jumped to the highest in two decades, but renewed worries about weak private consumption are likely to temper any optimism about the economy.
"USD/JPY is likely to fall steeply if there is no change in policy," Sean Callow, senior currency strategist at Westpac in Sydney, said in a note to clients. "Most likely there will be at least some tweaks of the existing suite of policies."
The dollar edged up 0.2 percent to 111.61 yen, moving back toward a three-week high of 111.90 notched on Monday.
The euro was steady at $1.1324.
U.S. crude futures were down 0.2 percent in early Asian trading at $45.22 a barrel, after hitting their 2016 high of $45.62 following the Fed's decision. Brent also rose to the highest for this year at $47.45, but shed 0.3 percent in Asian trade to $47.04.
Earlier in the session, the Reserve Bank of New Zealand kept its benchmark interest rate unchanged at 2.25 percent, but reiterated further easing may be needed given weak inflation.
The decision propelled the New Zealand dollar up 1.6 percent to $0.6919, after it rocketed as high as $0.6944.
Brazil's central bank also left interest rates unchanged late on Wednesday, leaving its benchmark Selic rate at 14.25 percent for the sixth straight meeting in its fight against high inflation in what could be the current board's last decision ahead of that country's likely change of government.