"The New Zealand Defence Force is committed to making this process as dignified and respectful as possible for the families of those being repatriated," Nixon said.
The three defence force members were Engineering Mechanic 1st Class Russell James Craig Moore, Flight Lieutenant George Thomas Beban, and Leading Aircraftman Ralph Henry Scott.
Moore died in an accident on HMNZS Lachlan in 1956 and was buried in Pago Pago, American Samoa.
"We are grateful to the government of American Samoa for agreeing to the disinterment and for caring for the resting places of our people for all these years.
"We would also like to thank the US Army's detachment in American Samoa for providing logistical support."
Beban died of natural causes in Fiji in 1956, while serving at RNZAF station Laucala Bay. He was 40.
Scott was also posted to the Laucala Bay RNZAF station when he died, aged 28, of natural causes in 1960.
Equality was the core principle throughout this process, Nixon said.
"We will have no preferential treatment regardless of background, status, wealth, or cause of death. This will ensure the inequalities that resulted from an inconsistent approach in the past are not repeated."