His era-changing victory came as he swept a series of key battleground states, winning Virginia, Pennsylvania and Ohio.
"We are, and always will be, the United States of America," he said.
He said it was time to put "hands on the arc of history and bend it once more to the hope of a better day.
"It’s been a long time coming but tonight, because of what we did on this day, in this election, at this defining moment, change has come to America," Mr Obama said.
He said he had received an "extraordinarily gracious" call from his Republican rival John McCain, who he said had "fought long and hard" for this campaign and for his country.
"We are better off for the service rendered by this brave and selfless leader," he said of the former Vietnam prisoner of war.
"I congratulate him, I congratulate Governor (Sarah) Palin for all that they’ve achieved.
"And I look forward to working with them to renew this nation’s promise in the month’s ahead."
He paid tribute to his running mate Joe Biden and said he would not be standing on stage tonight without "my best friend of the past 16 years, the rock of our family, the love of my life, the nation’s next first lady, Michelle Obama".
"Sasha and Malia, I love you both more than you can imagine and you have earned the new puppy that’s coming with us to the White House," he said to cheers from the crowd.
He also said he knew his 86-year-old grandmother Madelyn Dunham, who helped raise him but died of cancer late on Sunday night, would be watching.
Mr Obama also thanked his campaign manager David Plouffe, whom he described as an "unsung hero" who "built the best political campaign, I think, in the history of America.
"To the best campaign team ever assembled in the history of politics, you made this happen and I am forever grateful for what you’ve sacrificed to get it done," he said.
"Above all, I will never forget who this victory truly belongs to : it belongs to you.
"I was never the likeliest candidate for this office ; we didn’t start with much money or many endorsements ; our campaign was not hatched in the halls of Washington."
He said his campaign "began in the backyards of Des Moines (Iowa)" and was built by working men and women "who dug into what little savings they had" to give small donations to the campaign.
"It grew strength from the young people who rejected the myth of their generations apathy, who left their homes and their families for jobs that offered little pay and less sleep.
"It grew strength from the not-so-young people who braved the bitter cold and scorching heat to knock on doors of perfect strangers.
"And from the millions of Americans who volunteered and organised and proved that more than two centuries later a government of the people, by the people and for the people has not perished from the earth."
"This is your victory."
Delivering his message, Mr Obama told those whose support he had not won : "I hear your voices, I need your help and I will be your president too."
He told those watching outside the US that "our stories are singular but our destiny is shared.
"The new dawn of America leadership is at hand," he said.
"To those who would tear the world down, we will defeat you.
"To those who seek peace and security, we support you.
"And to all those who have wondered if American’s beacon still burns as bright, tonight we’ve proved once more that the true strength of our nation comes not from the might of our arms or the scale of our wealth but from the enduring power of our ideals, democracy, liberty, opportunity and unyielding hope.
"That’s the true genius of America."
Mr Obama said the challenges to come were "the greatest of our lifetime" - two wars, a planet in peril and a financial crisis.
"The road ahead will be long, our climb will be steep. We may not get there in one year, or even in one term, but America I have never been more hopeful than I am tonight that we will get there.
"I promise you, we as a people will get there."
He said there would be "setbacks and false starts" and the government would not be able to solve every problem.
But he said : "I will listen to you, especially when we disagree.
"Above all, I will ask you to join in the work of remaking this nation the only way it’s been done in America in 221 years, block by block, brick by brick, calloused hand by calloused hand.
"What began 21 months ago in the depths of winter cannot end on this autumn night.
"This victory alone is not the change we seek, it is only the chance for us to make that change. And that cannot happen if we go back to the way things were."
He called for a new spirit of patriotism and responsibility "where each of us resolves to pitch in and work harder and look not only after ourselves, but after each other".
He added the "great victory" was won "with a measure of humility and a determination to heal the divides that have held back our progress".
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