Mr Obama, 47, and his vice-presidential running mate Joe Biden were projected by television networks as winners in the swing states of Pennsylvania, New Hampshire, Ohio, New Mexico, Iowa and Virginia.
"The road ahead will be long. Our climb will be steep. We may not get there in one year or even one term, but America, I have never been more hopeful than I am tonight that we will get there," said Mr Obama.
"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."
"We have proved that the true strength of our nation comes not from the scale of our wealth but from the power of our ideals – opportunity, democracy, liberty and hope."
The Democratic nominee’s victory over his Republican opponent John McCain, possibly by a landslide margin, was an overwhelming rejection of President George W Bush’s eight years in office by Americans.
"A new dawn of American leadership is at hand," Mr Obama announced.
"To those who would tear the world down, we will defeat you. To those who seek peace and security, we support you."
The Republican candidate’s chances of winning the White House were doomed by a series of battleground state losses and he has already called Mr Obama to concede.
In a concession speech delivered in Phoenix, Arizona, Mr McCain congratulated Mr Obama on winning the presidency, saying "the American people have spoken."
US President George W Bush also telephoned his apparent successor to congratulate him on his "awesome night," said Dana Perino, a White House spokeswoman.
In Chicago, Obama campaign workers were hugging and congratulating each other at 10pm (3am in Britain).
The Democrat was expected to deliver a victory speech some time after polls in California closed.
A win for Senate Minority Leader Mitch McConnell in Kentucky was one of the few bright spots of the evening for Republicans, and kept alive their hopes of preventing a 60 to 40 majority for Democrats, which would make it impossible to block legislation without some Democratic help.
Six out of 10 voters said in an Associated Press exit poll that the economy was the most important issue facing the country, a concern Mr Obama has made the centrepiece of his campaign.
Officials said the long queues and heavy early voting in more than 30 states pointed towards a turnout of between 130 million and 140 million people, up from 121 million four years ago, and 65 per cent of those registered.
This would represent the highest percentage turnout since 1908. Mr Obama’s campaign, which heavily outgunned Mr McCain’s in terms of the number of volunteers, fund-raising and enthusiasm had poured immense resources into registering new voters.
High turnout was a key sign that David Plouffe, Mr Obama’s campaign manager, had succeeded.
Democratic gains of up to nine seats in the Senate would give Democrats the 20-seat majority they need to withstand Republican filibusters and herald a new period of untrammeled one-party rule in Washington.
A victory for Mr Obama, who began his bid for the White House nearly two years ago as an unlikely outsider, marks a landmark in the long struggle for racial equality in America. When he was born in Hawaii to a black Kenyan father and a white mother from Kansas in 1961, many American states banned interracial marriages. Four years later, blacks in many Southern states were disenfranchised.