Before a huge and emotional crowd in Grant Park, Chicago and the streets beyond, the 47-year-old first-time Democratic senator from Illinois acknowledged the historic nature of his victory yesterday, Sydney time.

He also seized the mandate he had received to take America in a different direction, both economically and in its dealings with the rest of the world, and so to leave the Bush era behind.

"We are and always will be the United States of America," he said. "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."

Many people in the crowd wept openly as Senator Obama honoured the civil rights activist Martin Luther King jnr, who had forged the path towards racial equality, and such unsung heroes as Ann Nixon Cooper, a 106-year-old African-American woman who voted on Tuesday and who was born just one generation after the end of slavery in America.

The transformative nature of Senator Obama's victory was acknowledged by his defeated rival, the Republican John McCain, who said Senator Obama had inspired the hopes of millions of Americans who had once wrongly believed that they had little at stake in the election of an American president.

"We both recognise that, though we have come a long way from the old injustices that once stained our nation's reputation and denied some Americans the full blessings of American citizenship, the memory of them still had the power to wound," he said.

Even as Senator Obama delivered his victory speech, he warned that the climb for America "will be steep".

Americans face huge challenges, including two wars, a planet in peril and the worst financial crisis in a century, he said.

But he also told the American people: "This is our moment. This is our time."

It was time "to put our people back to work", he said: "And open doors of opportunity for our kids; to restore prosperity and promote the cause of peace; to reclaim the American dream and reaffirm that fundamental truth that out of many, we are one; that while we breathe, we hope; and where we are met with cynicism and doubt and those who tell us that we can't, we will respond with that timeless creed that sums up the spirit of a people: Yes, we can."

Hundreds of thousands of people in Grant Park echoed the campaign chant, "Yes, we can".

Addressing the rest of the world, Senator Obama promised that America would defeat those who threatened it but would help countries who pursued peace.

He said America would return to what it truly stands for: "democracy, liberty, opportunity and unyielding hope".

At home Senator Obama will now hold the best chance of delivering on his pledges since Bill Clinton in the early years of his presidency because the Democrats control the White House, the Senate and the House of Representatives.

Top of his agenda will be expanding health care to cover the 47 million uninsured, kickstarting the economy, making the tax system fairer by giving middle-class Americans a tax cut, and working with the world towards a solution to climate change.

He is also likely to get the opportunity to reshape the Supreme Court with two appointments during his first term which would tip the balance away from conservative justices.

Senator Obama's win was emphatic. Even before the polls closed on the West Coast it was clear that he had won in the critical swing states of Ohio, Pennsylvania, New Hampshire and Iowa, and that he was leading in Indiana and Florida.

He will also pick up several states in the south-west and the Rockies that had previously voted Republican.

Senator Obama has won at least 338 electoral college votes, to 163 for Senator McCain, CNN said.

The result was achieved with a record turn-out.

Before the publication of official figures, voting experts and election officials estimated more than 130 million voters cast ballots, which would be the highest percentage voter turn-out in a century. The previous record was set four years ago, when 123.5 million people cast their ballots.

Senator Obama's rival during the primary season, fellow Democrat Senator Hillary Clinton, said it was an historic victory for the American people.

"This was a long and hard-fought campaign, but the result was well worth the wait," she said. "Together, under the leadership of president Barack Obama, vice-president Joe Biden, and a Democratic Congress, we will chart a better course to build a new economy and rebuild our leadership in the world."

Senator Obama was joined on stage behind bullet-proof glass shields by his wife, Michelle, and their two children, Sasha and Malia, as well as the vice-president elect, Joe Biden, his wife and their family.

Acknowledging his family's efforts, the president-elect said he would deliver on his promise to get a puppy for the White House.