Mr Bainimarama and his FijiFirst Party secured 32 out of the 50 seats in parliament and an outright majority, the election office said.
His closest rival, Sodelpa Party, won 15 seats.
Wednesday's polls were the first in Fiji since Mr Bainimarama seized power in a coup in 2006.
International observers have described the election as credible, conducted in a "atmosphere of calm" with an absence of electoral misconduct or "evident intimidation".
FijiFirst took 59.2% of the vote, the Fijian Elections Office said, with an election turnout of almost 84%.
Official results were delivered on Monday but by Sunday Mr Bainimarama had claimed victory.
Promising to govern "for the wellbeing of all Fijians", he also paid tribute to the military.
"It is because of their legacy that today we have a democratically elected parliamentary government," he said.
Fiji has seen four coups since 1987 attributed mainly to tensions between indigenous Fijians and ethnic Indians.
In 2006, Mr Bainimarama ousted the elected government of Laisenia Qarase, accusing it of corruption and bias towards indigenous Fijians. Since then, Fiji has been under military rule.
Mr Bainimarama said he wanted to end the instability and in these elections discarded the race-based voting system.
His authoritarian rule is seen to have brought stability and economic growth to the country.
But human rights groups accuse him of placing severe restrictions on freedom of speech through media censorship and intimidation of critics, as well as interference with the judiciary.
Regional allies Australia and New Zealand have long been calling for polls to take place.
Fiji's former military leader Frank Bainimarama has been sworn in as prime minister of the Pacific nation after an emphatic election win.