Tech-heavy markets such as Japan, Taiwan and South Korea were among the region's best performers as Apple's earnings report and strong sales forecast backed views consumer demand is recovering.
Apple's shares surged more than 5 percent to an all-time high of $257.30 in after-hours trade.
European shares were also seen rising in an Apple-fueled rally -- Futures for STOXX Europe 50, Germany's DAX and France's CAC 40 were 0.3 to 0.4 percent higher.
Before Apple released its numbers, U.S. stocks rose by as much as 0.8 percent in the regular session as higher oil prices lifted energy shares and as investors saw generally stronger company results as a sign that the global economy was recovering.
The euro, which has been slipping since last week on concerns about Greece, fell 0.1 percent to $1.3420 and is now in danger of revisiting its March low of $1.3267 sometime soon.
Greek yields hit 12-year highs as Athens prepared to launch talks on an EU/IMF bailout package aimed at rescuing Greece from a debt crisis rocking the euro zone.
The Canadian dollar rose to a near two-year high after the Bank of Canada signaled the day before an interest rate rise may come as early as June, and it climbed 0.2 percent against the yen, outperforming other crosses.
The generally upbeat sentiment about demand sparked a rally in commodities and global growth-linked currencies such as the Australian dollar, which was strong against a range of currencies, including the euro, where it tested record highs.
Oil rose past $84 a barrel, buoyed by optimism about the global economic recovery and an unexpected drop in U.S. fuel inventories. That optimism helped gold which added to its ongoing recovery from a near two-week low hit on Monday.
If people are going out and buying iPhones, Macs and iPads the hope is the U.S. consumer is going to start consuming again, said Andrew Sullivan, a sales trader with broker MainFirst Securities, adding this was also boosting shares of big exporters.
That probably means the recent trend of increased U.S. savings is possibly not as strong as people had worried about, he said, referring to fears that the U.S. economic recovery might be shaky until shoppers started hitting the stores again.
The MSCI index of Asia-Pacific stocks outside Japan <.MIAPJ0000PUS> rose 1 percent, with the regional tech index <.MIAPJIT00PUS> up 2.2 percent.
Industrial shares <.MIAPJIN00PUS> and raw materials stocks <.MIAPJMT00PUS> were the other outperformers on signs of stronger demand, gaining a little over 1 percent.
In Tokyo, the Nikkei average <.N225> registered its biggest one-day percentage gain in over a month as chip-related stocks like Toshiba Corp <6502.T> leapt. The yen's decline against the dollar helped the export sector in general. Toshiba gained nearly 3 percent.
The Japanese yen remained subdued at 93.29 per dollar, after falling 0.8 percent on Tuesday.
The yen, which tends to gain in times of greater risk aversion, had risen to a near one-month high of 91.58 per dollar earlier this week as global stocks retreated on concerns that they had risen too far, too fast in recent sessions.
Taiwan stocks <.TWII> logged their best one-day percentage gain in three weeks and South Korea's benchmark index <.KS11> closed at a 22-month high.
The euro edged down to $1.3420, from $1.3443 late in New York on Tuesday, when it fell 0.3 percent. It fell 0.2 percent against the yen.
Ten days of talks will begin on Wednesday on the belt-tightening measures Greece must take until 2012, the European Commission said, paving the way for the swift payout of up to 30 billion euros of euro zone emergency aid if Athens asks for it.
The yield spread between Greek and German 10-year bonds widened to a record 489 basis points from 468 bps on Monday, according to Tradeweb.
(Editing by Kim Coghill and Ron Popeski)