There are hopes the US will bounce back, helping exporting firms
Asian stocks have risen following the election of Democrat Senator Barack Obama as the next US president.
Japan's Nikkei 225 index closed 4.4% up, Hong Kong's Hang Seng rose 3.2% and Singapore's benchmark index added 2.6%.
The climbs came after the US Dow Jones index had risen 3.3% on hopes a new leadership would help the US economy as it faces the threat of a recession.
There are expectations the Democrats will speed up economic measures to boost the world's largest economy.
The dollar also strengthened on the news. One euro was worth $1.2873, whereas earlier it had been worth $1.2975. The pound fell to $1.5866 after earlier trading at $1.5997.
And Australia's main stock index ended up 2.9%.
However, not all markets rose. India's Sensex index fell about 5%, and in Europe, where shares had risen strongly on Tuesday, the markets were also down. Both the FTSE 100 in London and the Cac 40 index in Paris were down by about 3%.
Shares in New York rose on Tuesday as people in the US went to the polls for the presidential election. The Dow Jones Industrial Average closed up 305.5 points at 9,625.3.
Doug Kass, founder and president of hedge fund Seabreeze Partners Management, said the Wall Street rally was an "Obama bounce, not an Obama rally".
"It's growing clear that the recession is going to have a shelf life unlike the last recessions in both scope and duration," he added.
Rob Henderson, head of market economics with National Australia Bank in Sydney, said: "Well, it can't be negative for markets. It's a vote for change and has to inject a degree of optimism that America can again reinvent itself."
However, other analysts were less optimistic.
Kircy Daley, senior strategist of Newedge Group in Hong Kong said: "The knee-jerk complacency rally in Asia to an Obama win is likely creating an opportunity to sell.
He said economic fundamentals in the US were "deteriorating faster than the market can keep up with. And there is very little an Obama administration can do to shield Asia from the effects of this downturn."
As the US economy has slowed, Asian exporting firms - a mainstay of the region's economies - have been hard hit.