British Prime Minister Gordon Brown has said he is looking forward to working with US president-elect Barack Obama.
He said the Democratic senator ran an "inspirational campaign, energising politics with his progressive values and his vision for the future".
Conservative leader David Cameron hailed Mr Obama as the "first of a new generation of world leaders".
Liberal Democrat leader Nick Clegg said the outcome of the US elections was "vital to our future".
In a statement, Mr Brown also paid tribute to the Republican candidate, senator John McCain.
He said he fought a "good campaign and has shown the characteristic dignity that has marked a lifetime of service to his country".
Mr Brown, who held talks with Mr Obama in London during the summer, added: "The relationship between the United States and the United Kingdom is vital to our prosperity and security."
Mr Brown said: "I know Barack Obama and we share many values.
"We both have determination to show that government can act to help people fairly through these difficult times facing the global economy."
Higher education minister David Lammy, who knows Mr Obama after meeting him at a Harvard alumni event in 2005, told the BBC the election of the first black American president was a "watershed moment in history".
He said: "Martin Luther King's dream was that people would be judged not by the colour of their skin but by the content of their character. Today, Dr King's dream has come true."
Mr Cameron said the US presidential race had been an "exciting and inspirational contest".
He said: "In electing Barack Obama, America has made history and proved to the world that it is a nation eager for change.
"In these difficult times people everywhere are crying out for change.
"Barack Obama is the first of a new generation of leaders who will deliver it - he has my whole-hearted congratulations.
"This is an important moment not just for America but for the world. Barack Obama's victory will give people a new opportunity to look at the United States and see her for what I believe she is - a beacon of opportunity, freedom and democracy."
'Hopes and expectations'
Responding to Mr Obama's victory, Mr Clegg said: "British voters may not have been able to vote in this election, but its outcome is vital to our future.
"Climate change, the global economy, and threats to our collective security now demand a radical new approach by Barack Obama, leaving the Bush era firmly behind.
"The world will not succeed in this era of globalisation without the leadership of the new American President.
"The weight of peoples' hopes and expectations on Barack Obama is immense."
Scotland's First Minister Alex Salmond sent a message to Mr Obama offering his "heartfelt congratulations" on a "wonderful and historic" election victory.
"It ushers in a new era of hope for the United States and its role in the world. This was a victory for optimism over pessimism, for hope over fear," he told him.
Challenges ahead
First Minister for Wales Rhodri Morgan said Barack Obama's "stunning victory represents a triumph of hope over fear".
He said Obama now has two months to prepare for the "huge job of translating that hope into improved conditions for jobs and health domestically for America".
The United States' Ambassador to London, Robert Tuttle, said it had been a great night for democracy and freedom in America.
"I always thought until last night that the most exciting election that I'd ever seen was Kennedy versus Nixon in 1960 but it was far eclipsed by last night," he said.
