The dollar sat at more than 66-month lows against the pound after a strong set of manufacturing figures out of Britain.
Investors are also eyeing the release later in the week of closely watched US jobs figures that will provide fresh clues about the strength of the recovery in the world's number one economy.
Tokyo rose 0.29%, or 43.77 points, to 15,369.97, Sydney added 1.48%, or 79.5 points, to 5,455.4 and Seoul put on 0.81%, or 16.28 points, to close at 2,015.28.
Shanghai ended 0.44%, or 9.04 points, higher at 2,059.42 while Hong Kong advanced 1.55%, or 358.90 points, to 23,549.62.
US shares jumped in response to news out of China that a survey of manufacturing activity in June hit its highest level this year, suggesting a growth slowdown may have bottomed out. Traders were also boosted by surprisingly strong figures for US auto sales.
The Dow climbed 0.77% on Tuesday and the S&P 500 added 0.67% — both ending at all-time highs. The Nasdaq surged 1.14%.
Investors were unfazed by the Institute for Supply Management's manufacturing purchasing managers' index of manufacturing activity, which dipped marginally in June.
Focus now turns to the release of non-farm payrolls figures from the US Labor Department.
"Upcoming US jobs data should help to reinforce hopes that the US economic recovery remains on track," Mizuho Securities senior technical analyst Yutaka Miura told Dow Jones Newswires.
On currency markets, the dollar headed back towards 102 yen after sinking over the past few days. In New York on Tuesday the greenback rose to 101.53 yen from 101.40 yen in Tokyo earlier in the day.
In Asian business on Wednesday the unit sat at 101.55 yen. The euro bought $1.3678 and 138.90 yen in Tokyo against $1.3677 and 138.88 yen in New York.
The dollar was also under pressure against the pound after a surprise rise in British manufacturing data for June.
The pound bought $1.7147 in Tokyo after hitting $1.7166 late Tuesday, the highest level since October 2008.
Currency dealers have been moving into the pound in recent weeks after the head of the Bank of England suggested interest rates could rise sooner than initially thought as the economy picks up pace.
On oil markets US benchmark West Texas Intermediate for August delivery rose five cents to $105.39, while Brent crude dipped six cents to $112.23 in afternoon trade.
Gold fetched $1,326.03 an ounce at 1040 GMT compared with $1,325.00 late Tuesday.
In other markets, Taipei rose 0.46%, or 43.04 points, to 9,484.96. Taiwan Semiconductor Manufacturing Co gained 3.52% to T$132.5, while Hon Hai Precision Industry closed 0.98% higher at T$103.
Wellington was marginally higher, adding 3.12 points to 5,149.39. Chorus edged up 0.58% to NZ$1.735 and Fletcher Building ticked 0.23% higher to NZ$8.77.
Manila ended up 0.35%, or 23.99 points, at 6,850.60. Ayala Corp rose 1.47% to 9.50 pesos, Alliance Global added 0.51% to 29.35 pesos, and Bank of the Philippine Islands gained 1.85% to 93.50 pesos.
Mumbai surged 1.27%, or 324.86 points, to 25,841.21 points. Adani Ports gained 10.98% to 270.90 rupees, while Castrol India rose 8.94% to 361.20 rupees.
Kuala Lumpur rose 0.41%, or 7.72 points, to 1,886.84. SapuraKencana Petroleum added 1.4% to 4.40 ringgit, while utility Tenaga Nasional rose 1.5% to 12.38.
The Stock Exchange of Thailand added 0.41%, or 6.06 points, to 1,491.81. Bangkok Bank gained 3.37% to 199.50 baht, while convenience store operator CP All lost 3.12% to 46.50 baht.
Jakarta ended up 0.48%, or 23.45 points, at 4,908.27. Property firm Ciputra Development gained 3.21% to 965 rupiah, while miner Aneka Tambang slipped 0.91% to 1,090 rupiah.
Singapore rose 0.66 percent, or 21.27 points, to 3,263.91. Singapore Airlines rose 1.16% to S$10.49 while Oversea-Chinese Banking Corporation was up 0.32% to S$9.48.