The remains were removed from Lake Mungo in the Willandra Lakes area of southwest NSW without the approval of traditional owners between 1960 and 1980.
Among them were remains known as Mungo Man and Mungo Lady, discovered in 1974 and 1969.
Mungo Lady's remains show evidence of one of the world's oldest known cremations and Mungo Man is the oldest human skeleton to be discovered on the continent.
Both also provided knowledge of ritual burials.
"While the discovery of Mungo Man and Mungo Lady helped scientists establish that Aboriginal people have been in Australia for more than 42,000 years, it's time to let their spirits rest in peace," NSW Heritage and Environment Minister James Griffin said.
The discovery of the remains paved the way for Mungo National Park to be declared a UNESCO World Heritage Site, which delayed the reburial.
Reburial required approval under Commonwealth law, and Environment Minister Sussan Ley announced in August the federal assessment of a Willandra Lakes Region World Heritage Area Aboriginal Advisory Group (AAG) and NSW government plan.
The remains have been held in a safe since being returned in 2017.
AAG chair Patsy Winch welcomed the approval.
"Finally, after all that time has passed, the voices of the elders have been heard and I am thankful that these ancestral remains will finally be laid to rest the traditional way, in Country," Ms Winch said.
She said future projects offered the chance for traditional owners to work with scientific and university institutions with respect and harmony.
The reburial will be supported through Heritage NSW and the National Parks and Wildlife Service.
