The discovery was made in the country’s north-western Turkana region.
Mr Kibaki said it was “the first time Kenya has made such a discovery” and called it a “major breakthrough”.
Kenya is a regional business and tourist hub with the largest economy in East Africa, although its relative wealth is not based on mineral riches.
The Kenyan president said Tullow would drill more wells to establish the commercial viability of the oil.
“It is… the beginning of a long journey to make our country an oil producer, which typically takes in excess of three years. We shall be giving the nation more information as the oil exploration process continues,” he said.
Tullow Oil, which also struck oil in neighbouring Uganda, said the Kenyan find had exceeded their expectations.
“This is an excellent start to our major exploration campaign in the East African rift basins of Kenya and Ethiopia,” said Angus McCoss, the company’s exploration director.
He added: “To make a good oil discovery in our first well is beyond our expectations and bodes well for the material programme ahead of us.”
Tullow has found oil in, or off the coast of, a number of African countries, including Ghana and Sierra Leone.