Many Asian investors were hopeful that the president would focus renewed energy on tackling deteriorating economic conditions in America - a vital export market for Asian goods - and the worst financial crisis in decades that has dragged on growth around the world.
Analysts said the markets' gains weren't necessarily driven by a preference for Obama over Republican rival John McCain. It was more relief that came with the end of the long U.S. presidential campaign, coupled with rising confidence that as the credit crunch eases world equities markets could see a year-end rally after October's brutal sell-off.
Obama's win "is an excuse for the market to rally. There's less political uncertainty and that gives investors more confidence in the short term," said Frank Gong, a Hong Kong-based managing director for JP Morgan Securities. "But technically it's more about the credit crisis settling down and the market's fear coming down."
Some analysts said the next administration would be hard pressed to deliver a quick fix to the many U.S. economic woes.
"Changing the president is not going to be enough to save the American economy," said Kazuo Mizuno, chief economist at Mitsubishi UFJ Securities Co. in Tokyo.
He said the U.S. is likely to need financing from Japan, China, the Middle East and other countries if it hopes to fund public bailouts for its financial system and deliver on tax breaks and other measures needed for recovery.
"Even the president is not going to be able to change America without help from the world," Mizuno said.
With Asian countries heavily reliant on exports for growth, there's also the potential for trade friction should the Democratic party, in charge of the White House and Congress, back protectionist policies, analysts said.
"Obama has at times sounded protectionist, and time will tell whether this will meaningfully impact the further development of trade links around the world," Moody's economist Sherman Chan in Sydney wrote in a research note.
While benchmarks in Britain, Germany and France dropped 1 percent or more in early trade, most Asian stock markets closed higher. Japan's Nikkei 225 stock average advanced 4.5 percent to 9,521.24, and Hong Kong's Hang Seng Index added 3.2 percent to 14,840.16.
Australia's main stock index rose 2.9 percent, and Singapore's key stock measure added 2.6 percent. India's Sensex dropped 2.8 percent.
In South Korea, the benchmark Kospi rose 2.4 percent, though pared gains on profit-taking and some concerns that an Obama presidency could mean a harder line on trade, analysts said.
The upswing followed Wall Street, where many investors looked past more signs of a slumping U.S. economy and piled into stocks.
The Dow Jones index staged its biggest Election Day rally ever, rising 305.45 points, or 3.3 percent, to close at 9,625.28. The broader indices also rose, with the Standard & Poor's 500 index up 39.45, or 4.1 percent, to 1,005.75, its first close over the 1,000 mark since Oct. 13.
Wall Street futures were down, suggesting a lower open in the U.S. Wednesday. Dow futures were down 120, or 1.3 percent, at 9,461, while S&P futures were down 14.8, or 1.5 percent, at 988.4.
In Japan, a weaker yen boosted shares of major exporters including automakers and consumer electronics firms. Toyota Motor Corp. rose 10.3 percent, Canon Inc. jumped 11.7 percent and Sony Corp. advanced 6.3 percent.
The dollar was trading at 99.14 yen, up from the 98-yen zone the previous day in Asia.
Sanyo Electric Co. surged 18 percent after being untraded Tuesday due to a rush of buy orders triggered by weekend reports that the company may be bought by rival Panasonic Corp.
A Sanyo-Panasonic entity would create Japan's biggest electronics maker, surpassing Hitachi Ltd., and would also be among the biggest in the world. Officials from both companies denied Tuesday that any deal has been reached.
Oil prices retreated after surging above $70 a barrel overnight. Light, sweet crude for December delivery was changing hands at $67.30, down $3.23 in Asian trade on the New York Mercantile Exchange.
AP Business Writers Yuri Kageyama in Tokyo and Kelly Olsen in Seoul contributed to this report.