There is a carnival atmosphere across the country
Kenya has declared Thursday a public holiday to celebrate the election of Barack Obama to the US presidency.
Mr Obama's father was from Kenya and his victory has prompted jubilation across the country.
"We the Kenyan people are immensely proud of your Kenyan roots," President Mwai Kibaki said.
The BBC's Juliet Njeri says Mr Obama's step-grandmother was seen dancing and cheering jubilantly outside her house after the results were declared.
She says Mr Obama's family stayed up all night in the western Kenyan village of Kogelo watching the election count, and they are now preparing for a big party.
African leaders from South Africa to Somalia have sent their congratulations to the US president-elect.
Nelson Mandela, South Africa's first black president, welcomed Mr Obama's victory as a sign of hope for everyone.
"Your victory has demonstrated that no person anywhere in the world should not dare to dream of wanting to change the world for a better place," he said in a letter of congratulations.
In Kisumu city, near the Obamas' home village, there is a carnival atmosphere and people have poured onto the streets singing Mr Obama's praises, our reporter says.
Political leaders are expected to join massive celebrations planned in the city, which considers Mr Obama their chosen son, she says.
In January, Kisumu was the scene of running battles between members of the public and police after riots broke out over the Kenya's contested elections.
But correspondents say the US election seems to be a unifying moment for the country, with people reported to be saying that Mr Obama's victory is a victory for all Kenyans.
In the capital, crowds were seen singing and dancing, waving branches and carrying posters of Mr Obama along Ngong Road, one of Nairobi's major highways.
"Your victory is not only an inspiration to millions of people all over the world, but it has special resonance with us here in Kenya," Mr Kibaki said.
Barack Obama's election success is celebrated
Mr Obama's victory is being celebrated across the continent.
South African Archbishop Desmond Tutu said it showed "that for people of colour, the sky is the limit".
The BBC's world affairs correspondent Adam Mynott says Mr Obama will inherit a foreign policy legacy in Africa that has been one of the high points of the George Bush administration.
Earlier this year President Bush toured through five African nations and people greeted him in their thousands to applaud him for America's huge contribution in the fight against HIV/Aids.
Since its launch five years ago, his Aids relief programme has spent more than $15bn dollars (£9.5bn) on the continent and saved many thousands of lives.
He says Africans will look to Mr Obama to deliver more when he takes office in January, and his difficulty will lie in matching the soaring expectations.