The Chinese yuan struck a 28-month peak as the US dollar hit a 10-week low.
Shares have surged, oil prices have jumped and the US dollar has remained weak as expectations of fewer regulatory reforms and more monetary stimulus under US President-elect Joe Biden supported risk appetite.
The dollar has hit a 10-week low as investors heralded Biden's election victory by buying trade-exposed currencies on expectations that a calmer White House could boost world commerce and that monetary policy will remain easy.
The Chinese yuan struck a 28-month peak, the New Zealand dollar made a 19-month high and the Australian dollar hit a seven-week top as the dollar index fell to its lowest since early September.
The South Korean won hit a 21-month high of 1,115.33 per dollar. Sterling hit its highest in more than two months while the euro rose 0.1 perecent, extending an almost 2 percent gain from last week to hit a two-month high of $1.1895.
Biden crossed the threshold of the 270 electoral college votes required for victory on Saturday by winning the battleground state of Pennsylvania. Republicans appear to have retained control of the Senate, though the final makeup may not be clear until runoff votes in Georgia in January.
"The outcome is ideal from a market point of view," said CMCMarkets' chief strategist in Sydney, Michael McCarthy. "Neither party controls the Congress, so both trade wars and higher taxes are largely off the agenda."
The prospect of more gridlock also means that expectations for a massive US fiscal stimulus package have been lowered, which has sent bond yields sharply lower in anticipation of less borrowing and more quantitative easing from the US FederalReserve.
The broad dollar weakness had the yen a touch firmer against the US dollar and just below Friday's eight-month peak of 103.18 yen per dollar, while lower US bond yields also made Treasuries less attractive to prodigious buyers in Japan.
The yuan, particularly sensitive to the election outcome because of a perception that Biden will take a softer or more predictable line on China, was also boosted by strong Chinese trade data over the weekend to stand at 6.5826 per dollar.
"The undertow of dollar weakness is probably going to have a bit of a way to run in terms of the Fed and also less trade tension as something positive for other currencies," said Westpac currency analyst Sean Callow.
Larger moves were held in check on Monday because currency markets had largely reacted to Biden's victory on Friday and because Donald Trump, the first incumbent to lose a re-election bid in 28 years, has made no sign of conceding.
"We would caution that heightened volatility is not necessarily behind us, even though the election result is all but settled," said Commonwealth Bank of Australia currency analyst Kim Mundy in a note.
The president, who has spent months trying to undermine the election results with unproven allegations of fraud, pledged on Saturday to go forward with a legal strategy that he hopes will overturn state results that gave Biden the win.
Traders are also wary as coronavirus cases surge, with the global tally of infections topping 50 million on Sunday as cases in the United States surpassed 10 million - stoking worries of more lockdowns.