The bones are believed to be the remains of four Aborigines, one of whom lived 10,000 to 15,000 years ago.
In 1986, Ted Bailey, a high-tech boomerang-maker from Ann Arbor, found the bones among Aboriginal artifacts he received in a trade from a Cleveland man who could not afford to pay cash for some boomerangs.
When the bones left Australia and how they got to the Cleveland man remain unclear. Road-builders apparently unearthed the bones from a grave, and someone stole them.
"It may have been an accidental find," Bob Weatherall, one of two Aborigines who participated in Wednesday's ceremony, told The Ann Arbor News. "But the theft was premeditated."
Weatherall said the search to recover such remains is spiritual and part of a battle to preserve their culture.
"We are fighting and trying very hard to be able to maintain these customs and beliefs," he said.
To collectors, the bones might be a curiosity. To the Aborigines, who flew to Detroit on Sunday, the bones represent their ancestors and are a haunting reminder of brutalities and indignities suffered at the hands of their continent's European settlers.
Bailey said he did not realize the cultural sensitivity about the bones. In 1999, Bailey got the idea to put them up for auction on eBay, to see if anybody else had an interest in them.
"They were on there for about a day," he said, "and I started getting e-mail from Aborigines who were very upset about it."
Bailey was ready to mail the remains to whoever wanted them in Australia, but he quickly heard from an Australian government official.
The official said he could not just mail human remains and suggested giving them to an intermediary, C. Loring Brace, the curator of biological anthropology at the University of Michigan's Museum of Anthropology.
Two of the bones will be returned to the land of Weatherall's people, the Gummaliroi, in eastern Australia. The other two were those of members of the Yorta Yorta people and will be returned to southeastern Australia.
There are thousands of remains of Aborigines in institutions in Australia, as well as more than 5,000 in Britain and 2,000 in the United States, Weatherall said.
The subject of returning native remains and artifacts is a hot issue in the United States as well as in Australia. Congress passed legislation in 1990 that required museums to notify American Indian communities of artifacts in their collections.