"We have accepted the verdict of the majority in the referendum," Ruto said at a news conference.
Claiming victory, Kiraitu Murungi, the country's energy minister and director of the "yes" campaign, said that Kenyans had spoken with a "thunderous voice" and that "Kenya has been truly reborn".
Mwai Kibaki, the president, backed the victory when speaking in front of hundreds of supporters at a rally.
"The historic journey that we begun 20 years ago is now coming to a happy end," Kibaki said in central Nairobi, the capital.
The new constitution addresses corruption, political patronage, land grabbing and tribalism, which have plagued Kenya since it won independence in 1963.
Responding to the developments, Catherine Ashton, the EU bloc's foreign affairs chief said that the vote for a more democratic constitution represented a "landmark" in Kenya's reform agenda, "which demonstrates the commitment of the government to fundamental legal and political change".
Andrew Simmons, Al Jazeera's correspondent in Nairobi, said this was a victory for all Kenyans.
"It is really a case whereby not only can the 'yes' campaigners claim victory, but Kenyans as a whole can celebrate a victory of common sense and a political maturity," he said.
"No one would compare this directly with the 2007 hotly contested elections, but it was a test case because there was a lot of resistance to this constitution and there were fears there would be violence.
"The voting passed by peacefully and the results it would appear would seem likely that there would not be any violence."
Kenya's electoral authority pledged on Tuesday that the process would be more transparent than the 2007 national election, which was marred by claims of fraud in favour of Kibaki. Those allegations 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.
Despite the assurances, several hundred people in the country's Rift Valley fled their homes before the vote, fearing a flare-up of violence. The valley is home to a large concentration of "no" voters.
It was also the site of some of the worst attacks during the last election. Tribesmen used bows and arrows to fight each other, gangs hacked opponents to death and police were accused of shooting sprees.
The new charter was a key provision of the power-sharing deal struck in 2008 between Kibaki and Rail Odinga, Kenya's prime minister and former opposition leader.
Ruto, Odinga's former ally and a cabinet minister based in the Rift Valley, spearheaded the "no" campaign, saying provisions in the new bill relating to land ownership were unfair.
Kibaki and Odinga both back the "yes" campaign, putting two of the country's major ethnic groups onto the same side.
The draft constitution cuts down the president's enormous powers by setting up an US-style presidential system of checks and balances - part of the reason the draft appears to have wide support.