George W Bush has declared victory in the US presidential election after his Democratic challenger John Kerry admitted defeat.
President Bush and Senator Kerry spoke on the phone earlier
"I am proud to lead such an amazing country and I am proud to lead it forward," Mr Bush said in Washington.
Mr Kerry publicly admitted defeat in a speech in Boston.
He earlier telephoned Mr Bush to concede the state of Ohio, whose 20 Electoral College votes held the key to victory in the cliffhanger election.
Mr Bush said Mr Kerry had run a "spirited campaign" and was "gracious" in defeat.
He set out a conservative social and economic agenda for his second four-year term, singling out tax reform, social security and education as priorities.
He said the US would "help the emerging democracies of Afghanistan and Iraq to grow in strength and freedom".
"And then our servicemen and women will come home with the honour they have earned," he added.
The president said he wanted to reach out to all Americans, and he made an appeal to those who had voted for his opponent.
"I will need your support and I will work to earn it," he said.
"We have one country, one constitution and one future that binds us. When we come together and work together there is no limit to the greatness of America."
Ohio the decider
In his concession speech a short while earlier, Mr Kerry said he and Mr Bush had spoken "about the danger of division in our country and the need, the desperate need, for unity".
He told supporters: "Today I hope we can begin the healing."
Soon after Mr Bush's victory speech, UK Prime Minister Tony Blair congratulated President Bush, and spoke of the need to strengthen ties between the US and Europe.
With Ohio, Mr Bush has 274 Electoral College votes, four more than needed for victory. Mr Kerry has 252 votes.
Results are still awaited in New Mexico and Iowa but they cannot affect the outcome.
There was a delay of several hours in declaring Ohio a win for Mr Bush, because the Democrats said there was a substantial number of uncounted absentee and provisional ballots that could still have clinched it for Mr Kerry.
But in his concession speech, Mr Kerry said it had become clear that there were not enough outstanding votes for him to win Ohio.
He said it was vital that every vote must count and be counted, but the outcome should be decided by voters, not a protracted legal process.
"I would not give up this fight if there was a chance we would prevail," Mr Kerry said.
The result means Mr Bush has a stronger mandate than four years ago, when he won only after a 36-day legal battle over a recount in Florida.
In 2000, Mr Bush finally won Florida by 537 votes, but this time he won an undisputed victory, with a projected five-point lead over Mr Kerry.
President Bush will begin his new term in January with strengthened Republican majorities in both houses of Congress.
Senate Democratic leader Tom Daschle lost his South Dakota seat - the first such defeat for a party leader in more than 50 years.
The election gave the Senate its biggest-ever minority representation, with one African-American and two Hispanics elected to the 100-member chamber. Minorities also gained seats in the House of Representatives
The whole of the House and one third of seats in the Senate were at stake.
Eleven states also approved constitutional amendments to ban same-sex marriage.
Projections put turnout in the presidential election at more than 115 million voters - 10 million more than in 2000.
The projected vote showed Mr Bush leading Mr Kerry nationwide by three-and-a-half million votes.