Kenyatta, who is facing charges of crimes against humanity, took 50.07 percent of the vote, narrowly avoiding a round of runoff elections, The Washington Post reported.
His main rival, Prime Minister Raila Odinga, took 43.28 percent of the vote.
Before the results of the election were announced, officials from Odinga's Orange Democrat Movement party said that if Kenyatta is named the winner, they will file a legal challenge of the results, the BBC reported.
"The level of the failures in the system makes it very difficult to believe it was a credible result, and if Uhuru is declared president, Raila will go to court," Salim Lone, one of Odinga's aides, told the Daily Nation newspaper.
"We are going to court," said Millie Odhiambo, an ODM parliament member. "You concede only when there is a credible process. But this was not a credible process."
Kenyans voted on Monday in the country's first presidential since 2007, when accusations of vote-rigging led to violent ethnic clashes in which more than 1,100 people died. Kenyatta has been accused by the International Criminal Court of inciting some of the violence.
If Kenyatta's win is upheld, tensions could arise between Kenya and the United States and some European countries, The Washington Post said.
Officials in Washington and other countries have warned that there could be consequences if Kenya is led by someone indicted by the ICC.