The voting ends a hard-fought race that began nearly two years ago and has cost more than $2bn (£1.3bn).
Polls will begin closing in eastern states at 19:00 EST (00:00 GMT) – a winner could be known by midnight.
Polls show the race is neck and neck, although the president holds a slender polling lead in crucial swing states.
National polls by Washington Post/ABC News and the Pew Research Centre both give Mr Obama a three-point edge over his rival.
The two men do see two visions – two different mirages of a future America, shimmering hazily on the horizon. But the trouble is there really are two Americas existing now. And the gulf between them is getting wider.”
As many as 30 million voters have already cast their ballots, with more than 30 states allowing either absentee voting or in-person early voting.
On the stroke of midnight, the first votes were cast and quickly counted in the tiny village of Dixville Notch in New Hampshire. They resulted in a tie with five votes each for Mr Obama and Mr Romney.
‘Work not done’
Mr Obama has already voted in his adopted hometown of Chicago, becoming the first sitting presidential candidate ever to vote early. Mr Romney is expected to cast his own ballot in Belmont, Massachusetts, later on Tuesday.
The election is decided by the electoral college. Each state is given a number of electoral votes in rough proportion to its population. The candidate who wins 270 electoral votes – by prevailing in the mostly winner-take-all state contests – becomes president.
Two pundits prepared to stick their neck out and predict results in the swing states both foresee a win for Barack Obama. Larry Sabato’s Crystal Ballgives Obama 290 electoral college votes – 20 more than the 270 required to win – while Nate Silver at the New York Times’ FiveThirtyEight blog envisages Obama taking 307 votes.
There are conservative pundits who predict quite the opposite. One, Dick Morris, a former Democrat, foresees Mitt Romney picking up 325 electoral college votes. George Will of the Washington Post, puts Romney on 321. Meanwhile, from the liberal camp, Josh Marshall’s Talking Points Memo putsBarack Obama on 303.
A handful of websites that choose not to predict a result in “toss-up” states see a small advantage for Obama. The New York Times and theWashington Post both think Obama is able to rely on at least 243 electoral college votes, compared with 206 for Mitt Romney. Charlie Cook gives Obama 237 to Romney’s 191, while Real Clear Politics leaves a full 146 electoral college votes in the toss-up category, with Obama on 201, and Romney on 191.
Also on Tuesday’s ballot are a handful of state governors, one third of the seats in the 100-member US Senate and all 435 seats in the House of Representatives.
Republicans are expected to keep control of the House, while Democrats were tipped to do the same in the Senate.
The presidential candidates spent Monday frantically criss-crossing the crucial battleground states including Ohio, Florida, Iowa and Virginia, making final appeals to voters. Their task: Push their own supporters to the polls while persuading the sliver of undecided voters to back them.
In speeches, Mr Romney kept up his attack on Mr Obama’s record, reciting a litany of statistics he says illustrate the president has failed to lift the US economy out of the worst downturn since the Great Depression that followed the stock market crash of 1929.
“If you believe we can do better, if you believe America should be on a better course, if you’re tired of being tired… then I ask you to vote for real change,” Mr Romney told a rally in a Virginia suburb of the capital, Washington DC.
The president appeared at rallies with singer Bruce Springsteen and rapper Jay-Z. He acknowledged frustration with the still-lagging economy but told voters “our work is not done yet”.
“We’ve come too far to turn back now,” the president said in Ohio. “We’ve come too far to let our hearts grow faint… We’ll finish what we started. We’ll renew those ties that bind us together and reaffirm the spirit that makes the United States of America the greatest nation on Earth.”
With observers anticipating a close race, both sides have readied teams of lawyers for possible legal fights, especially in the critical battleground state of Ohio.
Some analysts fear the election will not be decided on Tuesday night if the state’s vote becomes mired in legal battles.
Mr Obama will hold his own election night rally at a convention centre in Chicago.