Thirty-five soldiers who died in the conflict lie in Malaysia's Terendak Cemetery, which sits inside a large, operational military base, and one other in Kranji War Cemetery in Singapore. In May last year, then prime minister Tony Abbott offered repatriation to the families and more than 30 of them have accepted the offer.
"The homecoming of their family member will be a very moving and emotional time, and their right to privacy, grief and reflection has been central in the government's planning," said Australia's Veterans' Affairs Minister Dan Tehan in a statement.
For families who decided not to take up the offer, their relatives' graves will be maintained in perpetuity as is the standard for all Australian war dead in cemeteries around the world, the government said.
Royal Australian Air Force planes will fly the remains back to a military base outside Sydney on June 2 where they will be received in a formal ceremony, followed by a private memorial service for their families.
Vietnam Veterans Association of Australia president Ken Foster said the families and the veterans community had been asking for the bodies to be reinterred for some time.
"It was the family members who started putting pressure and raising all sorts of questions about, 'Is there some way we can have these veterans brought home?'," he told the Australian Broadcasting Corporation. Foster added that the move would enable not just family but those who fought alongside the fallen to pay their respects. "A lot of the veterans would not be in the situation where they could go to Malaysia and visit the graves," he said.
"Now the families will have the choice of where they're reinterred and the local veteran community within Australia will be able to visit those graves whenever they want." Australian soldiers killed in World Wars I and II and the Korean War were buried near to where they fell but around the time of the Vietnam engagement this policy changed and bodies were usually brought home.
Almost 60,000 Australian military personnel fought alongside the United States in Vietnam, with 521 losing their lives. Of these, all but the 36 in Malaysia and Singapore were returned home.