Delighted supporters packed the stadium but riot police drove back others as they tried to get in without seats.
Police were also deployed in another part of the city to stop a rally by opposition supporters.
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