Opinion polls before Tuesday’s vote put opposition leader Odinga, 72, who lost elections in 2007 and 2013, and President Kenyatta, 55, neck-and-neck.
Voter turnout will be key in an election that many fear could descend into violence.
Kenyatta, who is seeking a second and final term in office, gave a televised speech Monday in which he urged the 19 million registered voters to cast their votes “in peace”.
"After you cast your ballot, please go home," he said
"Go back to your neighbour. Regardless of where he or she comes from, their tribe, their colour or their religion... Shake their hand, share a meal and tell them 'let us wait for the results,' for Kenya will be here long after this general election," said Kenyatta.
In 2007, Odinga's call for street protests after problems with the vote count triggered a widespread campaign of ethnic violence in which 1,200 people were killed and 600,000
This time around, hundreds of people have already left the capital Nairobi amid concerns about potential post-election violence.
"We are fearful because before there was rigging and that led to violence," said Christine Okoth, an orange-seller at the open-air market in Kisumu, where much of the 2007 violence took place.
Wilson Njenga, a central government official overseeing the western region, said police had received disaster equipment including first aid and gloves but insisted it was all part of normal contingency planning.
"We don't want to be caught flat-footed," he told reporters.
But Rebekka Rumpel, Kenya expert at London-based thinktank Chatham House, told FRANCE 24 that fears of a return to the 2007-2008 violence may be unfounded.
“It is unlikely that we will see levels of violence comparable to 2007/2008, as reforms of key democratic institutions and the devolution process have made elections more credible… over the past decade,” she said.
Key election official murdered
The campaign has been marred by dozens of violent incidents however, including the murder of a key election official.
Chris Msando, who was in charge of the electronic voting system, and appeared on TV to reassure the public it would work -- and couldn’t be hacked -- was found dead on 29 July.
The discovery of his tortured, strangled body in a forest “soured the atmosphere in Kenya in the final days ahead of the election”, Rumpel said.
On Friday two foreign political advisers to Odinga’s NASA party were arrested and deported.
Joseph Orengo, a senior NASA official, said that the deportations were part of a government plot to undermine the opposition’s attempts to verify the election result.
“This should be seen in the context that yesterday was like an operation, not simply (targeting) this national centre but looking for everybody who would want to work with us,” he told AFP.
Odinga has already said Kenyatta can only win if his ruling Jubilee Alliance party rigs the vote, a position that increases the chances of a disputed result and unrest.
Eyebrows were raised in June when an audit of the current, new electoral register, by accounting firm KPMG, revealed over a million dead voters.
In the Odinga heartland of Kisumu, 28-year-old potato seller Ruth Achieng said: "If he doesn't win, we are going to the streets and we’ll demonstrate. The ones that die, we'll just bury them and life will go on."
Odinga on Monday again raised fears about vote rigging, and warned that the deployment of at least 150,000 security forces across the country was meant to intimidate voters.
He also congratulated his “worthy opponent” on his campaign. “May the stronger candidate win tomorrow,” he said.
Elections as litmus test
The elections are widely seen as a litmus test of Kenya's progress since the disputed 2007 election.
Kenyatta, along with deputy president William Ruto, had been charged by the International Criminal Courtfor organising the 2007 violence but in 2014 the charges against him were withdrawn.
Elections in 2013 were largely peaceful, although Odinga did accuse Kenyatta's Jubilee Party of election fraud after massive glitches with the electronic voting system.
Both candidates hail from storied political families. Kenyatta is the son of Jomo Kenyatta, Kenya's first president, and Odinga is the son of Jaramogi Odinga Odinga, the country's first vice president.
(FRANCE 24 with AFP and REUTERS)