The money will also be available to descendants of deceased members of the Stolen Generation.
Tasmanian Premier Paul Lennon unveiled the details of the package, which would provide one-off payments to members of the stolen generation and their children.
About 124 Aborigines are expected to qualify for compensation.
Under the proposed package, descendants of deceased members of the stolen generation would receive $5,000 each, capped at $20,000 per family.
Announcing the package to the Aboriginal community in Launceston today, Mr Lennon said the move was a major step in the reconciliation process.
"The funding pool that I've announced today can't undo the wrong that was done but it certainly can help the members of the stolen generation know that today's generation acknowledges the fundamental, terrible wrongs that were done," he said.
The bill will be introduced to state parliament at the end of the month and Mr Lennon is confident it has the support to become law.
If passed, a national advertising campaign will be launched appealing to Aborigines who were taken from their families under assimilation policies in Tasmania to come forward.
An independently-appointed assessor will judge each case against set criteria.
To qualify, applicants must be Aboriginal and have been removed from their families between 1935 and 1975 for at least 12 months.
Children of deceased parents who fit the category are also eligible for compensation.
Response
Aboriginal elder and stolen generation spokeswoman Annette Peardon said the announcement elicited feelings of "sadness and gladness".
"At the end of the day money is not going to do much ... the pain and suffering will never end, and I can only hope and encourage the stolen generation members. If compensation is paid that is a way of acknowledgement by the government, it was reality, it did happen," she said.
The announcement fulfils an election promise made by Mr Lennon earlier this year.