Kaurna people of South Australia have become the first indigenous people in the country to be formally recognised as the traditional owners of parts of an Australian capital city.

Federal Court judge Debra Mortimer on Wednesday finalised the group's native title claim over areas of Adelaide, 18 years after it was first lodged, following an agreement between elders and the South Australian government.

Kaurna elder Katrina Karlapina Power called it a magnificent day for the state.

"It has been a long time coming, you know, since first contact. It is really fantastic," Ms Power said.

The final agreement recognises 12 Kaurna elders as the descendants of the Aboriginal people who owned the land when Adelaide was settled in 1836, but it does not give them ownership of the 4000sq km of land now.

As part of the settlement, the state will provide a sum on trust for the benefit of all Kaurna people, and funds for the repatriation of ancestral bones now housed in South Australian museums.

Ms Power said many people who had carried the baton on land rights were unable to savour the win as the case took so long to resolve.

"We die young so many of our older people are not here to see this, but it is really important, this is an investment in our children's inheritances both black and white," she said.

The elder said she hoped the decision would help give momentum to other land rights decisions with consequences for other capital cities.

"You only need one to do it and the rest of them will follow," she said.

The courtroom in Adelaide was overflowing for the decision.

New Deputy Premier Vickie Chapman and former Weatherill government minister for Aboriginal affairs Kyam Maher were in court to hear the decision.

"It's the first time this has occurred in relation to a capital city claim and shows the close relationship between the state and the Kaurna people," Ms Chapman said.

Ms Chapman said native title claims were undoubtedly a difficult, complex and emotional issue for Aboriginal people

"The determining is a positive step towards reconciliation and a commitment to bettering our state and helping to facilitate Aboriginal participation and economic development," Ms Chapman said.

The Kaurna made the application in 2000 for the native title claim for 10,500 square kilometres stretching from Yankalilla in the state's mid-south to the Clare Valley in the state's mid-north.

It recognises the indigenous people had rights and interests over the land before colonial settlement.

The agreement will be formalised when an indigenous land use agreement is registered with the court in the next month.