Members of the Aboriginal community packed the floor of the chamber to witness the passage of the legislation, which was supported by the Lower House last week.
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Led by Aboriginal elder Annette Peardon, they erupted in jubilation when the bill was passed without amendment and later gave three cheers to Premier Paul Lennon, who responded with a modest thumbs-up.
Ms Peardon has been campaigning on the issue for more than a decade and, fittingly, her birthday coincided with yesterday's long-awaited result.
"After many years of hard work we have taken a real step towards reconciliation and I am proud to be Tasmanian today," Ms Peardon said.
The unanimous result was a far cry from the vote to hand back Cape Barren Island to the Aboriginal people which split Legislative Council members down the middle.
In a moving speech, Rosevears MLC Kerry Finch said the time for divisiveness was over.
"Society cannot simply block out a chapter of its history," he said.
"If we were to try this approach inevitably the void will be filled with lies or conflicting, confusing versions of the past."
A proud Mr Lennon, keen to progress the issue to a resolution, said an independent assessor was expected to be appointed within weeks.
Victims of the stolen generation and the immediate families of deceased victims will have six months to lodge a claim with the assessor to share $5 million in compensation.
The Tasmanian Aboriginal Council's Michael Mansell laid a challenge to the leaders of other States and the Federal Government to take Tasmania's lead.
"No matter how much the Aboriginal community appeals to governments, we can only bring about change like this when there is political leadership in government," he said.
