But the winner will not be officially elected until Dec 17, and will not take office until January.
The system used to elect the president stretches back to the very beginnings of the US, but it has been widely criticised for enabling a candidate who loses the popular vote to win, as happened in 2000.
Under the electoral college system, each state has a number of votes which is linked to its number of members of Congress, and reflects its population.
The most populous state, California, has the most votes, 55, while other large states like New York and Florida each have 29. The least populated states, Montana, Vermont and Alaska, for example, have just three votes.
A presidential candidate needs 270 electoral college votes — a majority of the 538 available — to win.
All electoral votes are cast for the candidate that wins the state, no matter what the margin. The two exceptions are Maine and Nebraska, which use a tiered system where a single elector is chosen within each Congressional district and two electors are chosen by state-wide popular vote.
The system is why certain swing states are targeted more than others. Some 11 such states could go either way, with the three holding the most electoral college votes being Florida (29), Pennsylvania (20) and Ohio (18), an analysis by RealClearPolitics.com showed.
These will be the ones to watch overnight as the results come in, along with Michigan (16), North Carolina (15), Virginia (13), Wisconsin (10), Colorado (9), Iowa (6), Nevada (6), and New Hampshire (4).
The others lean to the Democrats or Republicans already, giving Barack Obama 201 votes and his Republican challenger Mitt Romney 191 in the race to the magic 270 needed to clinch the presidency.
Ten states with 142 votes are expected to support Obama, while 16 states with 127 votes are expected to support Romney. A further five, with 41 votes — Connecticut, Maine, New Jersey, New Mexico, and Washington — are considered likely to vote for Obama, while six states with 50 votes — Georgia, Indiana, Missouri, Nebraska, South Carolina, South Dakota — are likely to vote for Romney.
Maine, Minnesota, and Oregon, with their 18 votes, are also thought to lean towards Obama, while Arizona and Montana, with 14 votes, are thought to lean towards Mr Romney.
But the formal process does not take place on election day tomorrow. Instead, Americans cast votes for their choice of president and vice president by voting for correspondingly-pledged electors, who then formally elect the president on Dec 17.
The electoral college system was originally established to ensure states could maintain control over who was allowed to vote. But it can distort the vote.
In 2000, 1888, and 1876, the victor failed to get the most votes in the nationwide popular vote but still won the race. In 2000, Al Gore had 48.4% of the popular vote compared with George Bush’s 47.9%.