Millicent Owuor, 20, gave birth to the twins in south-west Kenya on the day Obama was re-elected.
A short distance from the hospital, at the Obama family’s ancestral village, people were celebrating his victory.
“I named the first twin Barack and the second one Mitt,” Owuor was quoted by Reuters as saying.
Owuor posed for photographers on Wednesday at the Siaya District Hospital with her twin boys.
She said she had named her twins after the winning and losing US presidential candidates in order to remember the day of the vote, Kenya’s Standard newspaper reports.
The US president’s father was born in Kenya and his step-grandmother, Sarah Obama, still lives in the village of Kogelo.
The residents of Kogelo sang and danced after Obama was declared the winner.
“The reason why he has won is because God has given it to him,” said Sarah Obama, who turns 90 this year.
“Secondly, he has got the knowledge to love all people, he doesn’t have the knowledge of division, that is why he has won.”
Barack Obama senior died in a road accident in Kenya in 1982.
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