Japan's Nikkei 225 stock average advanced 4.5 per cent to 9,521.24, and Hong Kong's Hang Seng Index added about 3.1 per cent to 14,840.16.
In New York, the Dow Jones industrial average plunged down 500 points on new worries.
The election result was not a surprise to traders in the US, who returned to concentrating with dealing with the reality of a weakening economy.
Gulf markets finished marginaly higher on Wednesday.
Obama will inherit an enormous budget deficit when he is inaugurated on January 20. Analysts said they the market is already growing anxious about who Obama selects as the next treasury secretary, as well as who he picks for other cabinet positions.
"A lot of the policy going forward is going to have an effect on the various sectors of the market," Joe Keetle, a senior wealth manager for Dawson Wealth Management, said.
Obama's victory means that industries such as oil and gas producers, utilities and pharmaceuticals may face greater regulation and even taxes, while labour unions and automakers are expected to benefit.
In addition, banks, insurance companies, hedge funds and the rest of the financial sector will almost certainly face attempts at a regulatory overhaul by the Democratic congress next year.
Analysts said the market was also growing uneasy in advance of the labour department's October employment report, to be issued on Friday. Economists on average expect a 200,000 drop in payrolls.