"Cast your vote and keep the peace," Kibaki said.
Kibaki is standing down after serving two terms as president, the BBC reported.
There are eight candidates running for president, including Prime Minister Raila Odinga and Deputy Prime Minister Uhuru Kenyatta, who are seen as the frontrunners.
"Let us send a clear message to the world that our democracy has come of age. A peaceful vote is a vote for a secure, prosperous and stable Kenya," Kibaki said. "To those who will not win, your country still needs you. There are many other roles you can play in our development endeavors."
This is the first election under Kenya's new constitution that was adopted in 2010 in an attempt to avoid ethnic clashes similar to ones that occurred in 2007, which led to more than 1,200 people being killed and an estimated 600,000 others being forced from their homes, the BBC said.
The government said about 99,000 police officers will be deployed around the country to maintain order at polling stations.
Should a candidate in the election take more than 50 percent of the vote, they will be declared the winner. However, if no candidate obtains more than 50 percent of the vote, there will be a run-off on April 11.
Notable deaths of 2014 [PHOTOS]