Following the first democratic election in eight years, he pledged to govern "for the well-being of all Fijians", saying the country had "embraced a new future" after a series of coups sparked by ethnic tensions that rocked the islands.
Although the final count from Wednesday's election has not been released, provisional results showed Bainimarama's Fiji First Party heading towards a clear victory.
"My fellow Fijians, as you know Fiji First has won the general elections and I will lead the new government to serve the nation," he told thousands of cheering supporters gathered in a sports stadium.
The former military strongman's victory declaration came after the Fiji Electoral Office put Fiji First on 59.1 percent after votes had been counted at 88 percent of the polling booths.
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This would give Fiji First 32 seats in the 50-seat parliament. The Social Democratic Liberal Party was a distant second at 28.3 percent.
"I give you my absolute promise that we will govern for the well-being of all Fijians," Bainimarama said.
"I am the prime minister for all Fijians. We have a vision of a prosperous, modern and an inclusive Fiji and we intend to achieve it.
Bainimarama said he would head to New York in the coming days to attend the United Nations General Assembly and "tell the world what we have just accomplished in Fiji.
"It will be a landmark occasion, because I promised the nation of Fiji and the international community that I will take Fiji to the first genuine democracy in our history and I have kept that promise.
In his speech today he specifically singled out the military "who have stood for the ideal of true democracy" as he acknowledged "their vision, their perseverance and their sacrifice"