Harris, who voted early by mail in her home state of California, is due later to address students at Howard University, a historically black college in Washington DC, where she was an undergraduate.
“To go back tonight to Howard University, my beloved alma mater, and be able to hopefully recognise this day for what it is is really full circle for me,” Harris said on a radio interview earlier.
If she wins, she would become the first woman, black woman and South-Asian American to win the presidency.
Trump would become the first president to win non-consecutive terms in more than 130 years. He is also the only president to be impeached twice and the first former president to be criminally convicted.
Exit polling by CBS suggests that around a third of voters said the state of democracy was their top concern, out of the five options given.
The economy ranked second, with three in 10 voters choosing it, according to the preliminary data.
Abortion and immigration followed on the list, while foreign policy was deemed the least important.
In Detroit, Michigan, one voter, Melissa Klein, told the BBC: “Women’s rights are a huge, huge issue for me. I’m a nurse, I work in obstetrics, I’d never want to see a world where we can’t help women get the life-saving work they need.”
In Las Vegas, Nevada, first-time voter Jasmine Perez, 26, said she had cast her vote for Trump.
“What really attracted me to Donald Trump is I’m a Christian,” Ms Perez told AP news agency. “I like that he openly promotes Christianity in America.”
Law enforcement agencies nationwide are on high alert for potential violence.
About 30 bomb threats hoaxes targeted election-related locations nationwide on Tuesday, more than half of them in the state of Georgia alone, reports CBS.