Outgoing President Uhuru Kenyatta, having served the constitutionally limited two terms, is backing one-time foe Raila Odinga, 77, to succeed him.
His decision followed a falling out with Deputy President William Ruto, 55, who had expected to be endorsed.
More than 22 million Kenyans have registered to vote.
There are several other elections happening at the same time and a mix-up of ballot papers in some areas for some of those votes has again raised questions about the organisation of the general election.
Polls are open for 11 hours from 06:00 local time (03:00 GMT). Anyone still in the queue at closing time will be allowed to vote.
The results of the last presidential election in 2017 were annulled after the Supreme Court ruled that the electoral commission had not followed the law when it came to the electronic transmission of the vote tallies from the polling stations.
Seven charts that explain Kenya ahead of elections
Judges ruled that “illegalities and irregularities” had taken place.
A re-run was won by Mr Kenyatta, but boycotted by Mr Odinga – the main opposition candidate at the time.
The chairman of the electoral commission, Wafula Chebukati, who was also in charge of the 2017 vote, has frequently tried to reassure Kenyans that his team will be up to the task this time.
But Monday’s logistical problems have increased the pressure on him.