INTERNATIONAL NEWS - Delighted supporters packed the stadium but riot police drove back others as they tried to get in without seats.
In another part of the city, police clashed with opposition supporters trying to hold a rally.
Opposition leader Raila Odinga, who boycotted an election re-run last month, mocked Tuesday's "coronation".
Mr Kenyatta was officially re-elected with 98% of the vote on 26 October but just under 39% of voters turned out.
The original election on 8 August was held over again after being annulled by the Supreme Court on grounds of irregularities.
What is the mood at the stadium?
Spectators inside Nairobi's Kasarani sports stadium were entertained by music and dance performances, while the military paraded.
However, there were scenes of chaos outside when people without seats tried to rush in and were driven back by police with tear gas and batons, with some officers 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 news agency reports.
