Mr Kenyatta, in office since 2013, took 54.3% of votes, ahead of his rival Raila Odinga, with 44.7%.
After the announcement, Mr Kenyatta called for unity, telling opposition supporters: "I reach out to you... We are all citizens of the same republic".
But the opposition rejected the results even before they were declared, calling the process a "charade".
However, it has been endorsed by international observers. Mr Kenyatta said they had ensured a "free, fair and credible election".
Meanwhile, angry protests have started in the city of Kisumu - an opposition stronghold - and in various slums of the capital Nairobi, including Kibera, where businesses are said to have been attacked.