Japan's Nikkei led the way with a rise of 1.1%, though some other regional markets remain out of favour as funds flock to assets in the western world.
The dollar climbed against the yen after the US trade deficit shrank to its lowest in four years, thanks mainly to a renaissance in energy production, prompting analysts to revise up forecasts for economic growth.
Barclays, for one, doubled its estimate for last quarter and now predicts growth of 3% annualised.
The figures offered investors reassurance that the Federal Reserve's decision to taper its asset buying was justified by fundamentals. Minutes of the Fed's December meeting are due later on Wednesday and markets will be hoping for a clear commitment to keeping rates low for a long time to come.
Underlining the brighter mood were reports that the International Monetary Fund will raise its forecast for global growth in about three weeks, breaking a depressingly-long run of downgrades.
All of which helped MSCI's all-country world stock index hit its highest since mid-2008. Both the Dow and the S&P 500 rose 0.6%.
That was enough to give most Asian markets a break from recent selling pressure. MSCI's broadest index of Asia-Pacific shares outside Japan added 0.44%.
Stocks in Shanghai, Singapore and Taiwan all made ground.
Yet the region again lagged European equity indexes, which hit 5-1/2 year highs on Tuesday, led by a near 3% jump in Spain. The FTSEurofirst 300 index of top European shares gained 0.8%.
Sovereign risks across the euro zone's periphery have been receding as longer-term borrowing costs fall to multi-year troughs.
Yields on Irish 10-year debt dropped to their lowest in eight years after the country's first debt sale since exiting its EU/IMF bailout drew hot demand.
Yet data out Tuesday also showed core inflation in the EU slowed to a record low of just 0.7% in December, fanning fears of deflation ahead of the European Central Bank's policy meeting on Thursday.
It was worries about inflation falling too far that led the central bank to cut interest rates in November.
"This month's data will help reinforce expectations that the ECB are ready and willing to take whatever steps they deem necessary to prevent the economy from slipping into deflation," said economists at ANZ in a note to clients.
"While we think that the ECB will remain on hold this week, we are expecting a very dovish statement from ECB President Draghi."
The uncertainty kept the euro pinned at $1.3625 and not far from its recent one-month low at $1.3570.
The dollar got a boost from the US trade numbers and climbed as far as 80.946 against a basket of currencies, highs last seen in early December. It rallied to 104.83 yen and away from two-week lows of 103.91 set on Monday.
In contrast, investors dumped the Canadian dollar after the country reported a much larger trade deficit than expected, in a blow to the economic outlook there. The dollar was up at C$1.0787 on Wednesday, the highest since mid-2010.
The improving news on global growth was generally positive for industrial commodities and oil.
Brent crude edged up 2 cents to $107.37 per barrel, having broken five straight sessions of losses on Tuesday. US crude firmed 21 cents to $93.88.
Gold slipped as a stronger dollar and the rebound in US stock prices prompted investors to take profits in bullion after five sessions of gains. Spot gold was at $1,228.26 an ounce, from a top on Tuesday of $1,245.25.