Polls for weeks had shown a knife-edge race between Harris and Trump, who at 78 would be the oldest ever president at the time of inauguration, the first felon president, and only the second in history to serve non-consecutive terms.
Harris, 60, would also be only the second Black and first person of South Asian descent to be president.
She made a dramatic entrance into the race when Biden dropped out in July, while Trump -- twice impeached while president -- has since ridden out two assassination attempts and a criminal conviction.
'Super excited'
A final overall result in the presidential race could still take hours -- or even days.
Casting a ballot in Arizona, Trump backer Camille Kroskey, 62, said she was voting in person due to concerns about voting fraud.
"I want to make sure I drop my ballot where it's going to actually land somewhere," she told AFP.
Harris will hold her watch party later at Howard University in Washington, a historically Black college that she attended as a student.
"I'm a black woman. I'm an American. I'm super excited about the possibility of her becoming president," a tearful Camille Franklin, who also went to the college, told AFP.
Trump has vowed an unprecedented deportation campaign of millions of undocumented immigrants, in a campaign full of dark rhetoric.
Harris has hammered home her opposition to Trump-backed abortion bans -- a vote-winning position with women.
The election was meanwhile being watched closely around the world including in the war zones of Ukraine and the Middle East, anxious to see how the next Oval Office occupant deals with the conflicts.