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Japan's Nikkei led the way with a gain of 1.2%, while Australian shares added 0.4% and Shanghai 0.5%. MSCI's index of Asia-Pacific shares outside Japan crept up 0.3%.
A mixed bag of economic data caused few frowns since it merely reinforced expectations the Fed will maintain the status quo when its two-day policy meeting ends on Wednesday.
Even the US dollar got a lift as dealers judged the prospect of easy money for longer had now been pretty much discounted following two months of losses.
Markets seem to be operating on the assumption that the Fed's policy statement will not challenge the growing consensus that any tapering of its $85 billion of monthly asset purchases will not start until March at the earliest.
Such an outcome would be taken as justifying the rallies in stocks and bonds seen in recent weeks and might have only a limited impact on prices in the near term.
But it also means markets are vulnerable to a surprise.
"With expectations of taper firmly kicked into 2014 the risk that the FOMC could decide to move earlier looks asymmetrical," said Patrick Perret-Greene, an analyst at Australia and New Zealand Bank.
"If the Fed does nothing tomorrow then nothing really happens but if they do something or even hint at moves in the not too distant future the effects could be dramatic."
The Fed's decision is due at 1800 GMT, though divining its true message may be tricky as no new economic forecasts are released and nor will Chairman Ben Bernanke be giving a news conference.
BE BORING, PLEASE
For now, markets are counting on the Fed being boring.
The Dow Jones industrial average ended Tuesday 0.72% higher at an all-time closing peak of 15,680.35.
The S&P 500 gained 0.56%, aided further by a jump in heavyweight IBM
The flow of economic data proved too mixed to offer direction. Industrial output bounced in Japan, but disappointed in South Korea due to strikes at auto makers.
In the United States, a measure of core retail sales showed surprising resilience in September, yet a grim survey of consumers highlighted the heavy toll the recent government shutdown had taken on the public mood.
In currencies, dollar bears looked exhausted after two months of selling and the currency bounced broadly. The dollar index reached a one-week peak of 79.667, having climbed 0.5% on Tuesday. Just last Friday, it had plumbed a nine-month low at 78.998.
"Fed meetings have not been friendly to the USD this year, with the dollar weakening following every meeting in 2013 with the exception of June," analysts at BNP Paribas wrote in a client note.
"However, with markets already having adjusted to a much more dovish view on the Fed outlook, we think the USD is likely to hold up better this time."
The euro slipped to $1.3737, pulling away from a 23-month peak of $1.3833 set just a few days ago. The dollar firmed to 98.18 yen, from its recent trough of 96.94.
Yields on the benchmark 10-year Treasury note were steady at 2.506% after dipping from a high of 2.5360 on Tuesday. The market has enjoyed a substantial rally in the past two months with yields falling all the way from 3%.
Spot gold edged back to $1,343.24 an ounce as the dollar gained, but is still up more than 7% from a three-month low hit mid-October.
Brent oil futures lost 36 cents to $108.65 a barrel while US crude oil dipped 58 cents to $97.62.
Traders termed this a consolidation after a big gain on Monday when reports of a sharp drop in Libyan oil exports rekindled worries over global supply.
