Bitcoin has also hit a record high while traders bet on potential tax cuts, increased tariffs, and rising inflation under Trump’s second term.
This election result will have a major impact on the global economy.
The Republican Party is also set to take control of the Senate, although there are still votes left to count.
The dollar has soared by about 1.4% against a host of different currencies, including the pound, euro and the Japanese yen.
In Japan, the benchmark Nikkei 225 stock index ended the session up by 2.6%, while Australia’s ASX 200 closed 0.8% higher.
The major US stock indexes also look likely to open sharply higher. That came after the Dow Jones Industrial Average, S&P 500 and Nasdaq all closed more than 1% higher on Tuesday.
Why is Bitcoin going up?
The value of Bitcoin has also jumped by $6,000 (£4,645) to a record high of $75,371.69, surpassing the previous high of $73,797.98 seen in March this year.
Trump has previously pledged to make the US the “bitcoin and cryptocurrency capital of the world”.
His approach stands in stark contrast with that of the Biden administration, which led a sweeping crackdown on crypto firms in recent years.
Trump had suggested that he would fire Gary Gensler, the chair of the Securities and Exchange Commission who has received a backlash online from advocates of the digital currency.
This is due to Mr Gensler’s agency introducing new rules around environmental disclosures, which have been paused, as well as legal action against crypto companies.
Trump has also said he plans to put billionaire Elon Musk in charge of an audit of governmental waste.
Mr Musk has long been a proponent of cryptocurrencies and his company Tesla famously invested $1.5bn in Bitcoin in 2021, although the price of the digital currency can be very volatile.
Tesla’s Frankfurt-listed shares rallied over 14% at the open on Wednesday. Mr Musk, Tesla’s top shareholder, has supported Trump throughout his electoral campaign.
Experts predicted a turbulent day elsewhere on financial markets, however, as a response to global uncertainty and Trump’s potential plans for the economy.
US bond yields, the return a government promises to pay buyers of its debts, also soared on Wednesday.
A bond is essentially an IOU that can be traded in the financial markets and governments often sell bonds to investors when they want to borrow money.
Analysts have suggested this could be down to traders expecting that some of Trump’s economic measures could lead to higher prices.
Donald Trump has said, for example, he would dramatically increase trade tariffs, especially on China, if he became the next US president.
Tariff impact
Some economists have warned that Trump’s proposals around trade would come as a “shock” to the UK economy.
Ahmet Kaya, principal economist for the National Institute of Economic and Social Research (Niesr), said it could be “one of the countries most affected” under such plans.
It estimates that economic growth in the UK would slow to 0.4% in 2025, down from a forecast of 1.2%.
Katrina Ell, director of economic research at Moody’s Analytics said: “Trump’s global trade policies are causing particular angst in Asia, given the strong protectionist platform on which more aggressive tariffs on imports into the US have been pledged.”
Trump’s more isolationist stance on foreign policy has also raised questions about his willingness to defend Taiwan against potential aggression from China.
The self-ruling island is a major producer of computer chips, which are crucial to the technology that drives the global economy.
In mainland China, the Shanghai Composite Index ended the day down 0.1%, while Hong Kong’s Hang Seng was down by around 2.23%.
Trump’s tax-cutting agenda has been broadly welcomed by large corporates in the US.
“We should see pro-business policies and tax cuts, in turn possibly driving up inflation and less rate cuts,” said Jun Bei Liu, portfolio manager at Tribeca Investment Partners.
Investors also have other key issues to focus on this week.
On Thursday, the US Federal Reserve is due to announce its latest decision on interest rates.
Comments from the head of the central bank, Jerome Powell, will be watched closely around the world.
On Friday, top Chinese officials are expected to unveil more details about Beijing’s plans to tackle the slowdown of the world’s second largest economy.
