But the charter leaves unchanged the voting rights of foreigners, who are unable to participate at the cantonal level.
Following the passage of a law in 2005, non-Swiss who have lived in the canton for eight years can vote in municipal elections.
The new constitution, regulating such things as the terms of elected office and the number of signatures needed to trigger a referendum, was backed by 54 percent of those voting.
Ballots were cast at polling stations, by mail and through the internet but less than a third of eligible citizens took part in the historic vote.
In 2008, Genevans backed the creation of an elected 80-member constituent assembly to draft the new constitution.
The new document was supported by 75 percent of the assembly’s members.
Among the key changes is an increase to five years from four for the term of office of elected MPs and cabinet ministers.
The constitution weakens the power of the executive by submitting all changes to the state administration to approval by the cantonal parliament.
It also changes the number of signatures needed to be collected to put an initiative on the ballot to four percent of electors (around 9,650 compared to the current requirement of 10,000).
Three percent of voters are needed to petition for a vote on an initiative (a slight increase) and the parliament is empowered to submit its own proposals to a referendum with a two-thirds majority vote with the support at least 50 MPs.
The requirement for children to stay in school until the age of 18 is one of the other notable measures in the constitution.
The constitution will enter into law on June 1st 2013 but it will take a period of five years to phase in all legal aspects of the new framework.