Democratic Senator Barack Obama has been elected the first black president of the United States, prompting celebrations across the country.

"It's been a long time coming, but tonight... change has come to America," the president-elect told a jubilant crowd at a victory rally in Chicago.

His rival John McCain accepted defeat, and called on his supporters to lend the next president their goodwill.

The BBC's Justin Webb says the result will have a profound impact on the US.

He says the American people have made two fundamental statements about themselves: that they are profoundly unhappy with the status quo, and that they are slamming the door on the country's racial past.

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Mr Obama appeared with his family, and his running mate Joe Biden, before a crowd of tens of thousands in Grant Park, Chicago.

Many people in the vast crowd, which stretched back far into the Chicago night, wept as Mr Obama spoke.

"If there is anyone out there who still doubts that America is a place where all things are possible, who still wonders if the dream of our founders is alive in our time, who still questions the power of our democracy, tonight is your answer," he said.

He said he had received an "extraordinarily gracious" call from Mr McCain.

He praised the former Vietnam prisoner-of-war as a "brave and selfless leader".

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"He has endured sacrifices for America that most of us cannot begin to imagine," the victor said.

He had warm words for his family, announcing to his daughters: "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."

But he added: "Even as we celebrate tonight, we know the challenges that tomorrow will bring are the greatest of our lifetime - two wars, a planet in peril, the worst financial crisis in a century.

"The road ahead will be long. Our climb will be steep. But America - I have never been more hopeful than I am tonight that we will get there."

Hours after Mr Obama's victory was announced, crowds were still celebrating on the streets of Washington DC and Mr Obama's hometown of Chicago.