The return of the artefacts is being hailed as a victory for the repatriation of human remains from overseas museums.
Tasmania's Aboriginal community has welcomed home the bundles, brought by two young representatives from London.
Delegates Adam Thompson and Leah Brown presented the bundles in a private Aboriginal ceremony at Risdon Cove in Hobart.
Mr Thompson said it was "an emotional moment". "It's a big thing for Tasmanian Aboriginal people," he said.
The bundles, made from animal skin and containing ash gathered from a human cremation site, were acquired around 1838 by Christian missionary George Augustus Robinson.
Their return follows the introduction this year of the British Human Tissue Act, which gave museums permission to repatriate remains for the first time.
The victory has steeled the community's resolve to repatriate "hundreds" more remains being held in museums throughout the world.
"The British Museum has set a standard," Mr Thompson said. "They made a moral decision to return the remains and we're hoping that that's going to put pressure on other museums to do the same."
Meanwhile Britain's Natural History Museum appears reluctant to return its collection of human remains despite negotiations with the delegation earlier this week.
Mr Thompson said he would continue to fight the museum for the return of ancestors' remains.