The ceremony took place in a packed stadium with police driving back other Kenyatta supporters trying to get in without seats.
Riot police were also deployed in another part of Nairobi to stop a rally by opposition supporters.
Opposition leader Raila Odinga mocked Uhuru Kenyatta’s “coronation”.
Raila Odinga boycotted the re-run of the presidential poll last month and says Uhuru Kenyatta was not elected legitimately.
Uhuru Kenyatta was officially re-elected with 98% of the vote on October 26 but just under 39% of voters turned out.
The original election on August 8 was held over again after being annulled by the Supreme Court on grounds of irregularities.
Chief Justice David Maraga said the August election had not been “conducted in accordance with the constitution” and declared it “invalid, null and void”.
The Supreme Court ruled that the result had been “neither transparent nor verifiable”.
However, Raila Odinga urged his supporters to boycott the second vote because he said no reforms had been made to the electoral commission since the original poll.
Correspondents say the election dispute has left Kenya deeply divided.
About 50 people are reported to have been killed in violence since the August ballot.
Raila Odinga had promised to hold a “memorial rally” in another part of Nairobi to honor those killed during the four months of political upheaval since the August vote.
According to the opposition leader, Uhura Kenyatta was elected by “just a small section of the country”.
There were scenes of chaos outside Nairobi’s Kasarani sports stadium when people without seats tried to rush in and were driven back by police with tear gas, and on horseback.
Big screens had been promised so that tens of thousands of people could watch the ceremony from outside the stadium but no screens were provided, AFP reports.
Inside the stadium itself, foreign dignitaries took up their seats in a calm, good-humored atmosphere.
Spectators were treated to musical performances and a military parade.
Ethiopian PM Hailemariam Desalegn and Rwandan President Paul Kagame are among a number of African leaders attending. Israel’s PM Benjamin Netanyahu is also expected in Kenya’s capital but for an event later in the presidential palace, the Jerusalem Post reports.
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