Polls have opened in the east of the country after a long and bitter campaign amid the coronavirus pandemic.
Some 100 million people have already cast their ballots in early voting, putting the country on course for its highest turnout in a century.
Both rivals spent the final hours of the race rallying in key swing states.
National polls give a firm lead to Biden, but it is a closer race in the states that could decide the outcome.
Both candidates are using the day as an opportunity to drive home the messages they have been hammering to voters for the last few weeks.
Trump, sounding a little hoarse, spoke to Fox News by phone, saying he felt good about his chances of victory and predicting he would win "big" in key states such as Florida and Arizona.
"I think we have a really solid chance of winning," he said. Asked when he would declare victory, he added: "When there's victory. If there's victory... there's no reason to play games."
Some commentators noted Trump sounded tired during the interview after a late-night rally in Michigan.
Joe Biden visited his hometown of Scranton in Pennsylvania - a key swing state - and addressed a crowd there, saying: "It's good to be home."
"We've got to restore the backbone to this country," he said. "The middle class built this country - Wall Street didn't."
To be elected president, a candidate must win at least 270 votes in the electoral college. Each US state gets a certain number of votes partly based on its population and there are a total of 538 up for grabs.