The two diggers remains were found near Passchendaele, Belgium in December 2015, alongside the remains of a British soldier. In recognition that the three soldiers were found together, the trio have been buried in a joint Australian and UK service.
The funeral took place after a commemorative ceremony at the Menin Gate, Ypres, Belgium, with the soldiers ceremonially present during the Last Post Ceremony.
Minister for Defence Personnel Darren Chester said he "was honoured to attend the ceremony, and pay tribute to to the service and sacrifice of these soldiers".
"It is extremely special that the remains of these men could lie under the historic Menin Gate prior to their burial," Minister Chester said.
The three men's identities have not been able to be discerned, despite extensive investigations by the Australian Unrecovered War Casualties - Army (UWC-A) team and the UK's Joint Casualty and Compassionate Centre. Minister Chester said efforts to find suitable family members to give comparison DNA has been "extremely challenging".
"The efforts of agencies and organisations in Australia and the UK to identify these soldiers is to be commended, and they will continue to work as new information comes to light," Minister Chester said.
UWC-A is the Australian Army's unit responsible for finding, recovering and identifying Australian service men and women who remain unaccounted for from all past conflicts.
The UWC-A is currently investigating a "large number" of cases in Papua New Guinea, France, East Timor and Indonesia.
Investigations can last several months or years, and finding out the identity of a soldier is generally the lengthiest part of the process.