The election commission said Mr Kenyatta had narrowly avoided a run-off in a credible and transparent poll.
He hailed his win as a "triumph of democracy".
Speaking at the Catholic University in Nairobi, Kenyatta said Kenyans were celebrating the "triumph of democracy, the triumph of peace, the triumph of nationhood" and he had "demonstrated a level of political maturity that surpassed expectations". He also called on rival Raila Odinga and other leaders to "join us in moving our nation forward".
Mr Odinga, however, said he would challenge the outcome in court. He asked his supporters to avoid violence.
The poll was seen as a critical test for Kenya, whose reputation as a stable democracy was damaged by violence that followed the 2007 election.
Hundreds of people were killed in that post-election violence after clashes broke out when Mr Odinga claimed he had been cheated of victory by supporters of President Mwai Kibaki.
Mr Kenyatta, Kenya's richest man and son of its founding president Mzee Jomo Kenyatta, stands accused of organising the bloodshed and is facing charges at the International Criminal Court (ICC).
He is accused of fuelling the communal violence that saw more than 1,000 people killed and 600,000 forced from their homes.
Western powers welcomed the peaceful vote.
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