While polls had shown the race on a knife edge, the Republican fared far better than his Democratic opponent Vice President Kamala Harris as results rolled in.
Both candidates picked up expected wins in safe states, but indications that the business tycoon was on course for a second term boosted the so-called Trump Trade.
While victory is not yet official, Trump claimed it in a speech in Florida, saying: "We are going to help our country heal... We have a country that needs help and it needs help very badly."
News that the former president's party had won control of the Senate boosted the prospect of sweeping tax cuts, more tariffs, and deregulation -- seen as a boost for the greenback.
The dollar jumped 1.5 percent to 154.38 yen, its highest since July, while it was also up more than one percent against the euro and more than three percent against the Mexican peso.
Bitcoin sprung $6,000 higher to a record $75,371.69, topping its previous peak of $73,797.98 in March.
Trump has pledged to make the United States the "bitcoin and cryptocurrency capital of the world" and to put tech billionaire Elon Musk in charge of a wide-ranging audit of governmental waste.
"The price of bitcoin has closely followed Trump's position in the polls and on betting markets," Russ Mould, an analyst at AJ Bell, said ahead of Tuesday's US election.
Investors are "potentially taking the view that a Republican victory would lead to a surge in demand for the digital currency", he added.
Analysts said a clean sweep of Congress and the White House for Trump and Republicans would likely boost the dollar and Treasury yields owing to his plans to cut taxes and impose tariffs on imports.
Peter Esho, economist and founder at Esho Capital, said: "The markets are scrambling to figure out what happens next, but for the time being, the market is pricing in a higher growth and higher inflation outlook."
'Trade and tariffs and taxation'
And Neil Wilson at Finalto trading group said: "Trade and tariffs and taxation would be the three Ts of the Trump Trade, followed by deregulation."
But he added: "Bear in mind as a caveat that the House is still up for grabs and Trump had complete control of Congress last time and it didn't mean he could do everything he said he world."
Such an outcome could provide a headache for Federal Reserve boss Jerome Powell as he continues his battle to bring inflation to heel, with Trump's plans considered inflationary.
The election comes as the central bank prepares to deliver its latest policy decision Thursday amid expectations it will cut interest rates by 25 basis points, having lowered them by 50 points in September.
The dollar's surge against the yen rallied stocks more than three percent in Tokyo at one point thanks to gains in exporters, while markets Sydney, Singapore, Taipei, Mumbai and Bangkok also rose.
However, there were losses in Shanghai, Seoul, Wellington, Manila and Jakarta.
Hong Kong was also well down -- at one point diving almost three percent -- on worries about the impact of a Trump presidency on China's economy and relations between Beijing and Washington.
London, Paris and Frankfurt all rose at the open.
US futures also rallied.
Traders had been given a strong lead from Wall Street, where all three main indexes climbed more than one percent.
While the result of the election is being closely followed globally, it is of real interest in China after Trump vowed to ratchet up a trade battle with the economic titan by imposing massive tariffs on goods from the country.
The vote comes as Chinese leaders hold a key meeting to hammer out a package of stimulus measures aimed at kickstarting growth and providing support to the colossal property sector, which is mired in a painful debt crisis.
Beijing said Wednesday it hoped for "peaceful coexistence" with the United States as Trump looked set for victory.
Key figures around 0810 GMT
Dollar/yen: UP at 154.00 yen from 151.60 yen on Tuesday
Euro/dollar: DOWN at $1.0735 from $1.0930
Pound/dollar: DOWN at $1.2871 from $1.3035
Euro/pound: DOWN at 83.40 from 83.82 pence
Tokyo - Nikkei 225: UP 2.6 percent at 39,480.67 (close)
Hong Kong - Hang Seng Index: DOWN 2.2 percent at 20,538.38 (close)
Shanghai - Composite: DOWN 0.1 percent at 3,383.81 (close)
London - FTSE 100: DOWN 0.7 percent at 8,225.33
West Texas Intermediate: DOWN 1.2 percent at $71.13 per barrel
Brent North Sea Crude: DOWN 1.3 percent at $74.56 per barrel
New York - Dow: UP 1.0 percent at 42,221.88 (close)
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