With the Israel-Hamas conflict so far showing few signs of spilling over into a wider war -- keeping oil subdued -- traders were able to turn their focus back to the economic outlook.
The Fed is widely expected to keep borrowing costs on hold, with observers saying there is growing optimism that it has run its course after more than a year of hikes that have helped bring inflation down.
Elevated bond yields are also seen as acting as a substitute for further tightening, though decision-makers have for some time warned that rates will likely need to be kept high to completely win the battle against surging prices.
"The Fed is done, not just for this meeting, but for the cycle and the next move will be a rate cut," said Saxo Asia Pacific's Charu Chanana in a commentary.
The post-meeting news conference "could be key here, and more push on the 'higher-for-longer' message could still come as officials try to avoid the market undoing the work it has done for the Fed".
"This could mean they could continue to leave the door open for further tightening if needed."
Kristina Hooper, at Invesco, said policymakers were also likely worried about going too far, telling Bloomberg News "there is a real risk that the Fed commits overkill if it hikes rates any more than it already has".
Hopes the Fed has finished hiking helped Wall Street, with all three main indexes rising for a second straight day.
Shanghai, Sydney, Seoul, Singapore, Bangkok, Taipei and Wellington all rose but Hong Kong dipped.
London opened higher, as did Paris and Frankfurt.
Tokyo rallied more than two percent after the Bank of Japan stopped short of fully tweaking its monetary policy on Tuesday, even as it hiked inflation expectations.
Officials announced a minor change to its yield curve control programme, which allows bonds to rise and fall within a certain band, though there had been talk it would widen that band.
The news battered the yen, and on Wednesday it continued to fall, hitting 151.72 per dollar, its weakest level since touching a 32-year-low 151.95 in October last year and spurring an intervention.
It also touched a 15-year low against the euro.
The yen has tumbled in 2023 against its major peers as the BoJ refuses to budge from its ultra-loose policy, even as the Fed and other key central banks pushed rates to multi-decade highs to combat inflation.
But it picked up in early Asian trade after currency official Masato Kanda said Tokyo was ready to move if needed to step into forex markets.
"We're on standby," he told reporters. "But I can't say what we'll do, and when -- we'll make judgements overall, and we're making judgements in a state of urgency."
- Key figures around 0810 GMT -
Tokyo - Nikkei 225: UP 2.4 percent at 31,601.65 (close)
Hong Kong - Hang Seng Index: DOWN 0.1 percent at 17,101.78 (close)
Shanghai - Composite: UP 0.1 percent at 3,023.08 (close)
London - FTSE 100: UP 0.4 percent at 7,350.37
Dollar/yen: DOWN at 151.32 yen from 151.68 yen on Tuesday
Euro/dollar: DOWN at $1.0562 from $1.0576
Pound/dollar: UP at $1.2151 from $1.2142
Euro/pound: DOWN at 86.93 pence from 87.08 pence
West Texas Intermediate: UP 0.5 percent at $81.39 per barrel
Brent North Sea crude: UP 0.5 percent at $85.48 per barrel
New York - Dow: UP 0.4 percent at 33,052.87 (close)
-- Bloomberg News contributed to this story --
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