Mr Sarkozy says Mr Obama's victory "has raised enormous hope" in Europe
European leaders have hailed the triumph of Democrat Barack Obama in the US presidential election.
French President Nicolas Sarkozy said the victory was "brilliant", while UK Prime Minister Gordon Brown hailed Mr Obama's "vision for the future".
German Chancellor Angela Merkel said the result was "historic", while the European Commission president called for "a new deal for a new world".
Moscow said it was expecting a "fresh approach" in US relations with Russia.
Mr Obama beat Republican John McCain to become the first black US president.
"At a time when we must face huge challenges together, your election has raised enormous hope in France, in Europe and beyond," Mr Sarkozy said.
The global financial crisis will be a big test for Barack Obama
"France and Europe... will find a new energy to work with America to preserve peace and world prosperity," the French leader acted.
In London, Mr Brown said: "The relationship between the United States and the United Kingdom is vital to our prosperity and security.
"Barack Obama ran an inspirational campaign, energising politics with his progressive values and his vision for the future."
Mrs Merkel said that the German government was "fully aware of the importance and of the worth of our transatlantic partnership".
Meanwhile, European Commission President Jose Manuel Barroso said the world now needed the EU and US to forge "a new deal" to tackle the continuing global financial crisis and other major issues.
"We need to change the current crisis into a new opportunity. We need a new deal for a new world," Mr Barroso said.
In Moscow, Russian Deputy Foreign Minister Grigory Karasin said "everyone has the right to expect a fresh approach from the United States to all the most important problems, including... relations with Russia".
With the economy in recession and the US at war on two fronts in Iraq and Afghanistan, Mr Obama faces profound questions that will require quick answers, the BBC's Kevin Connolly says.
The president-elect though will have at least one asset no other American president since John F Kennedy has enjoyed - a huge reservoir of international goodwill, our correspondent adds.