The document "will underpin the first genuine democracy in Fijian history" and enshrine the principle of one person one vote, the government said.
Fiji's military ruler, Prime Minister Voreqe Bainimarama, has repeatedly said such voting rights are needed to ease long-standing tensions between indigenous Fijians and the island nation's sizeable Indian minority.
Indians make up just under 40 per cent of the 900,000-strong population.
"It will be the supreme law of the country and pave the way for elections on September 30, 2014, conducted for the first time on the basis of equal votes of equal value," the government said in a statement.
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The new constitution, which makes provision for a 50-member parliament and elections every four years, also enshrines principles such as a secular state, freedom of speech and an impartial judiciary.
A draft version of the document, prepared by Kenyan academic Yash Ghai, had called for the military to remain apolitical but Bainimarama scrapped it earlier this year and ordered government lawyers to rewrite the constitution.
The military's role is "to ensure at all times the security, defence and well-being of Fiji and all Fijians", says the constitution.
The current regime, which rules by decree, also abandoned plans to hold an assembly of church, political and civil society groups to review the document before it was finalised, leading to allegations it was silencing dissenting voices in the nation-building process.
Australia-based Pacific historian Brij Lal said the public had not been given any say in the latest constitution.
"They're introducing major changes here that will change the political culture of Fiji and there's been no public input into it."
While Bainimarama has pledged to hold elections in September next year, a similar vow to hold a poll in 2009 was never honoured, resulting in Fiji being suspended from the Commonwealth and the Pacific Islands Forum.