"Trump, being a businessman, will actually promote pro-business legislation, like cutting taxes and also spending heavily on infrastructure", which could help growth in the US, the world's biggest economy, said Francis Lun, chief executive of Geo Securities.
As Trump gained the lead in the electoral vote count, share prices tumbled in Asia, which were open during the election results.
Trump has also promised generous tax cuts, particularly for the higher paid, and more infrastructure and defence spending.
By the time Trump was confirmed the victor and made his speech, financial markets had steadied. Investors had feared Clinton would implement curbs on drug pricing increases that could hurt drugmakers and biotechnology companies. Crude oil prices closed higher after being down earlier in the day.
"People realized that it is not the end of the world".
HCA, the nation's largest hospital chain, was down almost 11 percent, while Viagra maker Pfizer climbed more than 8 percent, the biggest gain in the Dow.
European shares opened strongly, with France's CAC 40 jumping 1.2 percent to 4,596.34 and Germany's DAX leaping 1.2 percent to 10,776.93.
At Wall Street's closing bell Tuesday, the S&P index was down by 5 percent. The dollar also recouped some ground, while assets that many investors search out at times of uncertainty, such as gold, came off earlier highs. It was at 105.74 yen after dropping to near 101 yen the day before.
The price of gold was up $10.20, or 0.8 percent, at $1,285.50 an ounce. The U.S. currency rose sharply to 19.75 Mexican pesos from 18.68 pesos.
The dollar also recovered in currency trading.
"If Trump is able to follow through with these suggestions, Mexican activity will suffer greatly", said Jane Foley, senior foreign exchange strategist at Rabobank International.
Trump doesn't formally take the reins of power until January but he will begin the transition to his presidency nearly immediately.
"Less chance of a Fed rate hike also helps keep investors smiling at the prospect of cheap money and accommodative global monetary policy stance for a while longer", said Mike van Dulken, an analyst at Accendo Markets.
Another point of interest will center on the U.S.'s trade relations with China and its impact across Asia. Trump's victory has raised concerns that the US and China might embark on a trade war of sorts and that protectionism around the world will grow.
Those concerns weighed heavily on Asian stocks.
Japan's benchmark Nikkei 225 index, among the biggest losers on Wednesday, erased its losses by rocketing 6.7 per cent to 17,344.42. Many Wall Street watchers had anticipated a rocky turn for the market in the event of a victory by Trump, who had been seen as more of a wild card for stocks. Last week, the USA stock market capped a nine-day losing streak as investors grew concerned that Clinton, considered the status quo candidate, might not win.
Asian stocks are deep in the red, with benchmark indexes in Australia, Hong Kong, India, Indonesia, Japan, New Zealand, Singapore, South Korea and Taiwan tumbling 2-5 percent.
For financial markets as a whole, Trump's victory is the latest manifestation of a backlash against globalization.
Mahon says "globalization and the liberal economic consensus is in full retreat" if Trump doesn't temper his views.
Traders are selling bonds to hedge against the possibility that interest rates, which have been ultra-low for years, could rise steadily again under a Trump administration, said Tom di Galoma, managing director of trading at Seaport Global Securities.