Tokyo's Nikkei 225 index, the regional heavyweight, gained 0.8 percent to 14,542 points while China's benchmark Shanghai Composite Index rose 0.6 percent to 2,252.04. Hong Kong's Hang Seng was off 0.1 percent at 22,951.41 and Seoul shed 0.1 percent to 1,992.71.
Traders were encouraged by signs China, an important market for its Asian neighbors, is recovering from its deepest economic slump since the 2008 global crisis.
Markets were buoyed by data Tuesday that showed Chinese auto sales, factory output and investment all improved in August.
Those indicators "cemented the view that the China economy has stabilized," said DBS Bank in a report.
Citigroup raised its China growth forecast for the current quarter to 7.8 percent from 7.4 percent but warned that the rebound could be short-lived.
Elsewhere, Sydney's S&P ASX 200 gained 0.5 percent to 5,225.70. Benchmarks in Thailand and Manila rose while Singapore, Jakarta and New Zealand declined.
Optimism was tempered by President Barack Obama's comments in a speech Tuesday in which he ordered the American military to stay prepared to attack Syria if needed.
That came after tensions that had pushed up oil prices eased Monday on hopes for a diplomatic solution following Syria's announcement it would accept a Russian plan to turn over its chemical weapons.
Concern over Syria had spooked investors who worry about Middle East tensions disrupting oil supplies.
On Wednesday, benchmark crude fell 49 cents to $106.90 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $2.13 to close at $107.39 on the Nymex on Tuesday.
In Europe, market benchmarks in Britain, Germany and France all ended higher Tuesday ahead of Obama's speech.
On Wall Street, the Dow Jones industrial average and Standard & Poor's 500 also gained. The Dow Jones industrial average rose 0.9 percent to close at 15,191.06. The Standard & Poor's 500 index rose 0.7 percent to 1,683.99. The Nasdaq composite rose 0.6 percent, to 3,729.02.
In currency markets, the dollar rose to 100.57 yen from 100.39 yen late Tuesday. The euro fell to $1.3257 from $1.3265.
Investors also are looking ahead to next week's meeting of the U.S. Federal Reserve. The central bank is widely expected to announce plans to start phasing out its support program for the U.S. economy.