Bitcoin sprung $6,000 higher to a record $75,371.69, topping its previous peak of $73,797.98 in March.
The dollar jumped 1.5% 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.
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.
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."