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The world erupted in joy and dance yesterday with the announcement that Senator Barack Obama had been elected as the first black president of the United States.

From the birthplace of Obama's father in Kenya to his former elementary school in Jakarta, as well as other major capitals around the world, local residents were celebrating the outcome of Tuesday's US election.

"This will change lives, not only here, but in the whole world," said Obama's 86-year-old step-grandmother, dressed in her best traditional outfit and visibly emotional as she took reporters' questions.

From Washington to Los Angeles, people danced in the streets, wept, lifted their voices in prayer and brought traffic to a standstill. They marvelled that they lived to see the day a black man was elected president.

"I was born in the civil-rights time. To see this happening is unbelievable. We've got the first black president. A black president!" said Mike Louis, a 53-year-old African-American who got teary-eyed as he watched the election results on a giant video board in Cincinnati's Fountain Square.

The celebrations were both large and small, but the sentiment was the same: pure joy over how far the country had come.

Obama, 47, appears to have a mandate to lead beyond his borders. Three-quarters of 22,500 people surveyed in 22 countries by the BBC in September supported him. Even before yesterday's election, French President Nicolas Sarkozy dubbed Obama his "buddy", and British PM  Gordon Brown credited his Democratic Party with "generating the ideas to help people through more difficult times".

Analysts said Obama was committed to a foreign policy of intense diplomatic engagement with allies and adversaries alike and an international approach to curb nuclear proliferation, terrorism and other challenges.

Obama has pledged to accelerate the withdrawal of US troops from Iraq, build up US forces in Afghanistan and ask allies to play a bigger role in the fight against a resurgent Taleban.

"Obama will have to resort to 'soft power' to persuade others to go along. He'll push diplomacy to new heights, but in the end adversary countries like Iran may not listen," said Assoc Prof Panitan Wattanayagorn, an international-relations experts at Chulalongkorn University.

In a number of areas, there will likely be continuity with the policies of President George W Bush.

Obama has described a middle path on China much like Bush's, seeking expanded contacts while pressing for economic concessions.

Chinese leaders are not expecting big changes, because Obama buys into a US consensus that China is "a one-party system that is fundamentally against American interests", said Shen Dingli, director of the Centre for American Studies at Shanghai's Fudan University.

Obama has criticised Russia for supporting breakaway Georgian territories while eschewing confrontational measures like expulsion from summits of the Group of Eight economic powers.

While he has promised greater engagement in the search for Middle East peace, he will likely be forced to wait until both Israelis and Palestinians sort out internal political conflicts. Israel will watch him to see how far he goes to accommodate adversaries like Iran.

"The basic difference is going to be style," said Edward Walker, a former US diplomat. "We've gotten a reputation of never listening to anybody."