An 18,000 additional police officers have been deployed to potential hotspots for the vote.
The new law addresses corruption, political patronage, land grabbing and tribalism, which have plagued Kenya since it won independence in 1963.
Fears of dissention
However Andrew Simmons, Al Jazeera's correspondent in Nairobi, said there are concerns that the results of the vote will not be accepted.
"The key issue is what sort of majority goes down here.
"It's clear that the 'yes' campaign was in the lead according to opinion polls but it's felt that there needs to be a majority of over 60 per cent ... to swing this through," he said.
"If it's not really a resounding victory there could be much dissention."
Kenya's electoral authority said on Tuesday the process would be more transparent than the 2007 national election, when claims the poll was rigged in favour of president Mwai Kibaki led to violence in which at least 1,300 people were killed.
Kibaki assured the country that security had been strengthened at polling stations to prevent any violence.
"We have now come to a defining moment in our nation's history...vote to determine the destiny of our country," he said in a television and radio address.
Politicians and analysts predict that the referendum will be largely peaceful, but several hundred people in the country's Rift Valley have already fled their homes before the vote, fearing a new flare-up.
The Rift Valley is home to the largest concentration of Kenyans planning to vote against the constitution and the site of some of the worst attacks during the last elections.
During the violence, tribesmen used bows and arrows to fight each other, gangs hacked opponents to death and police were accusedof shooting sprees.
The new charter was a key provision in the power-sharing deal struck in 2008 between then rivals Kibaki and prime minister Raila Odinga to end the violence that followed the election in 2007.
William Ruto, Odinga's former ally, a cabinet minister based in the Rift Valley, is spearheading the "no" campaign, which is angry with the clauses related to land ownership.
Kibaki and Odinga both back the "yes" campaign, bringing two of the country's major ethnic groups onto the same side.
Recent polls have consistently shown that a majority of Kenyans back the new constitution, and it appears likely to pass.
The draft constitution cuts down the president's enormous powersby setting up an American-style presidential system of checks and balances, part of the reason the draft appears to have wide support.