Romney won North Carolina, Idaho, Montana, Arizona, Kansas, Louisiana, Nebraska, North Dakota, South Dakota, Texas, Wyoming, Mississippi, Alabama, Tennessee, Arkansas, Kentucky, Indiana, West Virginia, South Carolina, Oklahoma, Utah, Missouri and Georgia, CNN projected.
With the victory, Obama faces a country with chronic federal deficits and debt as well as sluggish economic growth in the wake of a devastating recession and financial industry collapse that confronted him when he took office in January 2009.
Around the country, voters formed long lines at polling places after record numbers participated in early balloting, indicating a strong turnout.
Sporadic reports of irregularities included malfunctioning voting machines and other problems, including electoral hardships for some struggling to recover from the devastation of Superstorm Sandy in states in the northeast.
A judge in Philadelphia, a heavily Democratic city, ordered election officials to cover a mural of Obama at one school used as a polling location after Republicans complained the painting violated election laws.
Elsewhere in the city, GOP poll monitors were being escorted into precincts by sheriff's deputies after some observers had been denied access earlier in the day, said Tasha Jamerson, a spokeswoman for the district attorney's office.
In New Jersey, which permitted electronic balloting in the aftermath of last week's storm, the state chapter of the American Civil Liberties Union headed to court on Tuesday on behalf of voters who said their requests for an electronic ballot weren't being acknowledged.
Candidates usually take Election Day off, but both sides made public appearances even as voting was under way.
Obama visited a local Democratic election center in the Chicago area, while Vice President Joe Biden made "an unannounced but long-scheduled" stop in the key battleground state of Ohio.
Romney and his running mate, Rep. Paul Ryan, also arrived separately in Ohio, with Romney's campaign plane and Air Force Two, which carries the vice president, crossing paths at Cleveland's airport.
Only a handful of states were considered up for grabs and both candidates and their campaigns concluded an exhausting final sprint through them over the weekend and on Monday.
The barnstorming amounted to a montage of Americana electioneering, with Obama and Romney shouting themselves hoarse before boisterous crowds, joined by top surrogates and star power such as Bruce Springsteen singing for Obama and Kid Rock for Romney.
Emotion overtook the president at the end of the day.
His eyes welled with tears as he thanked the people "who've given so much to this campaign over the years," during a stop in Des Moines, Iowa -- a place where his first campaign gained an early foothold in his first run for the White House.
"You took this campaign and made it of your own and you organized yourselves block by block, neighborhood by neighborhood, county by county, starting a movement that spread across the country," Obama said wiping away tears as he talked.
For his part, Romney called Obama's record one of underachievement and failure, telling a cheering Virginia crowd at his second stop of the day that "almost every measure he took hurt the economy, hurt fellow Americans."
For Romney, a multimillionaire businessman seeking to become the nation's first Mormon president, the election concluded a six-year quest for the presidency.
Romney also failed in his first bid for the Republican nomination in 2008, then spent the next two years preparing for a second run that began in 2011 with a grueling primary campaign featuring a record 20 debates.
Romney, 65, shifted to the right for the primary race to overcome a broad field that included former House Speaker Newt Gingrich, former Pennsylvania Sen. Rick Santorum, Rep. Michele Bachmann of Minnesota, Texas Gov. Rick Perry, former U.S. Ambassador to China Jon Huntsman and businessman Herman Cain.
Romney declared himself "severely" conservative and adopted stances against abortion, gay marriage and a path to legal residency for undocumented immigrants while also opposing higher tax rates as part of a deficit reduction plan. His support remained steady -- though well below a majority -- throughout the primary campaign while opponents dropped out one by one until Romney emerged as the winner and claimed the nomination at the GOP convention in late August.