Mr Obama celebrated winning a second term by pledging that the next four years would see an upsurge in prospects for what he described as the greatest nation in the world at a rally in his home city of Chicago.
With his wife Michelle, daughters Sasha and Malia's and vice-president Joe Biden also on the podium at a euphoric election rally, Mr Obama – who was showered in ticker tape after the speech – predicted fights ahead over the country's urgent economic problems.
Mr Obama, who polled at least 303 votes to Romney's 206 in the electoral college that decides the presidential race, told his supporters: "More than 200 years after a former colony won the right to determine its own destiny, the task of perfecting our union moves forward.
"It moves forward because of you. It moves forward because you reaffirmed the spirit that has triumphed over war and depression, the spirit that has lifted this country from the depths of despair to the great heights of hope, the belief that while each of us will pursue our own individual dreams, we are an American family and we rise or fall together as one nation and as one people."
Mr Obama said his supporters had fought their way to victory, and thanked every citizen who had voted.
He added: "We know in our hearts that for the United States of America the best is yet to come."
Pledging to "fix" the long queues outside polling stations that led to many people being unable to vote, Mr Obama heaped praise on Mitt Romney, who had earlier phoned him to concede defeat.
He pledged to talk to his defeated rival and discuss how they could "work together to move this country forward."
Mr Obama called congressional leaders from both political parties to express his commitment to working together on curbing the deficit and reducing taxes.
He also praised the support of Michelle, though he joked he would not give in to his daughters' wishes for another dog.
He conceded that democracy in a nation of 300 million people could be "noisy and messy."
But he added: "These arguments we have are a mark of our liberty.
"We can never forget that, as we speak, people in distant nations are risking their lives right now just for a chance to argue about the issues that matter, the chance to cast their ballots like we did today."
Mr Obama wanted America to be seen as a generous and tolerant nation where an immigrant's daughter who pledges allegiance to the Stars and Stripes could achieve success as much as a boy from the streets of Chicago or a furniture worker's child.
But, he added, progress was "not a straight line" or smooth and spoke of the need for consensus to solve the problems as the country prepares to end its engagements in Afghanistan and recover from the recession.
He said: "By itself, the recognition that we have common hopes and dreams won't end all the gridlock or solve all our problems or substitute for the painstaking work of building consensus and making the difficult compromises needed to move this country forward. But that common bond is where we must begin.
"Our economy is recovering. A decade of war is ending.
"A long campaign is now over."
He pledged to be more receptive and, with the Republicans, reduce the deficit and reform taxation and the immigration system. He added: "We've got more work to do."
Speaking of his experiences in New York and New Jersey following Superstorm Sandy, Mr Obama continued that love, charity, duty and patriotism made had made America great.
He said: "I have never been more hopeful about America. I ask you to sustain that hope."
Watched by an audience of tens of millions, including excited crowds gathered in New York's Times Square and other major cities, Mr Obama added: "We are, and forever will be, the United States of America."
Prime Minister David Cameron, in Jordan, said: "Congratulations to Barack. I've enjoyed working with him. I think he's a very successful US President and I look forward to working with him in the future."
First Minister Alex Salmond said: "He is the candidate to best express that there is a new America emerging."
However, on Wall Street, stocks fell more than 2% amid uncertainty over the showdown ahead in Congress over Mr Obama's fiscal reforms.
In his concession speech, Mr Romney said: "This is a time of great challenge for our nation. I pray the President will be successful in guiding our nation."
British experts warned the Republican Party could face a generation out of the White House if it fails to soften its stance on immigration and appeal to minorities.
They said the party faces its worst electoral crisis in 50 years. The minority groups who gave Mr Obama 80% of their votes are on track to become a majority of the population by 2050.
Professor Iwan Morgan, head of US Studies at University College London, said: "The Republicans are very close to the day of reckoning."
l President Obama's tweet that he had won "four more years" became one of the most read messages ever on Twitter after it was retweeted at least 670,000 times by last night.