Much of the action was in currencies where the Mexican peso has become a touchstone for sentiment on the election as Republican Donald Trump's trade policies are seen as damaging to its export-heavy economy. Against a basket of currencies, the dollar was up 0.2 percent at 98.090.
The Dow Jones industrial average was up 70.29 points, or 0.38 percent, to 18,329.89, the S&P 500 gained 6.1 points, or 0.29 percent, to 2,137.62 and the Nasdaq Composite added 20.03 points, or 0.39 percent, to 5,186.20.
MSCI's broadest index of Asia-Pacific shares outside Japan added 0.4 per cent and Australia 0.6 per cent. Futures pointed to opening gains for the Nikkei while E-mini futures for the S&P 500 rose 0.4 perc ent.
At the end of a bruising election campaign, the Reuters/Ipsos States of the Nation poll gave Clinton a 90 percent chance of defeating Republican Donald Trump and said she was on track to win 303 Electoral College votes out of 270 needed, to Trump's 235.
While polls last week showed Mr. Trump closing in on Ms. Clinton's lead, at least five major polls on Monday showed Clinton still ahead.
Market participants cited projections from data firm Votecastr, which showed Clinton in the lead in several battleground states.
Both currencies have been on investors' radar since Trump said in October he would renegotiate the trilateral North American Free Trade Agreement (NAFTA) between the U.S., Canada and Mexico - an event that could have a negative impact on the economies of the latter two.
The market has been pricing in a win for Clinton, including a 2 percent jump in the S&P 500 on Monday after the Federal Bureau of Investigation maintained its view that no criminal charges were warranted in a probe over her email practices.
The Mexican peso hit record lows against the U.S. dollar in late September as the polls indicated a tightening race between Trump and Hillary Clinton ahead of the first presidential debate.
The MSCI World index added 0.1 percent, building on Monday's 1.6 percent surge, its biggest single-day jump in nearly 19 weeks.
"Historically, since 1927 USA total share returns have been strongest at an average 16.7 percent per year when there has been a Democrat president and Republican control of the House, the Senate or both". "The renminbi is likely to continue to drop against the US dollar and the euro due to capital outflows and the negative outlook for the Chinese economy", he said.
Kathy Lien, managing director of foreign exchange strategy at BK Asset Management, said in a note that the dollar's strength in the USA session and the rally in US equities suggested investors expected a Clinton victory.
"Historically, since 1927 USA total share returns have been strongest at an average 16.7 per cent per year when there has been a Democrat president and Republican control of the House, the Senate or both".
Safety play gold weakened, down 0.4 percent to $1,275.80 an ounce and yields on U.S. Treasuries touched a one-week high.
In contrast, bulk commodities extended their bull run with iron ore, coal and copper benefiting mightily from Chinese demand.
Oil took a knock from data showing a surprisingly large rise in crude stocks. US crude CLc1 eased 22 cents to $44.76, while Brent LCOc1 was untraded early in the Asian day.