Trump was declared the winner after passing the 270 electoral votes needed to take the presidency.
The Republicans also gained a majority in the Senate, giving Trump sweeping powers to cut taxes and impose tariffs on imported goods - judged as a positive for the US currency.
When New York opened for trading yesterday, the benchmark S&P 500 rose 2.1%, the Dow Jones industrial average increased 3.1%, and the tech-focused Nasdaq composite climbed 2.1% - all hitting all-time records.
"That's the Trump trade," Marta Norton, chief investment strategist at Empower Investments, told CNBC. "There's a lot of emotion, there's a lot of euphoria, based on perspective in markets today. And I think that doesn't necessarily mean that's the way markets are going to trade in perpetuity."
Shares in the president-elect's Trump Media & Technology Group, hours after revealing another heavy quarterly loss, increased by as much as 30% before losing ground in another volatile rally.
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