Official results released by the Fijian Elections Office today showed Fiji First securing 293,714 or 59.2 per cent of the total votes.
This would give the party 32 out of 50 seats in the new Fijian Parliament which is expected to sit within the next two weeks.
Main opposition party, the Social Democratic Liberal Party, also known as Sodelpa, was a distant second at 28.2 per cent.
Mr MCully said Fiji and New Zealand have a history of close ties and that he looked forward to continuing "our programme of re-engagement" with Mr Bainimara's Government.
Mr Bainimarama, 60, claimed victory when he spoke to thousands of cheering supporters gathered at a sports stadium in Suva on Sunday.
"I am deeply honoured and humbled that the Fijian people have put their trust in me to lead them into our new and true democracy," he told the crowd.
"My absolute promise (is) that we will govern for the well being of all Fijians."
Mr Bainimarama has been prime minister since 2006, after he seized power through a military coup.
A long-simmering rivalry between indigenous Fijian nationalists and minority ethnic Indians continues to run deep in Fiji.
The election, held last Wednesday, was praised by a 92-member multinational observer group despite claims from opposition parties of fraud.
The group, which includes 11 from New Zealand, had concluded its formal observations with the declaration of the ballot today.
However, they will continue to work on the final report, which is expected to be completed and released within two months.
