Premier Paul Lennon is expected to announce details of the funding package -- the first of its kind in Australia -- at 1pm AEST.
The draft bill will be presented to members of Tasmania's Aboriginal community at the Tasmanian Aboriginal Centre.
It's believed the package -- tipped to be worth about $4 million -- will be disseminated by an independently-appointed assessor who will judge individual cases against set criteria.
At least 40 people are believed to have valid claims.
The package compensates Aborigines taken from their families under assimilation policies, mostly between the 1930s and 1950s.
Tasmanian Aboriginal Centre legal adviser Michael Mansell welcomed the package, but said no amount of money could compensate the suffering of members of the stolen generation.
"They were deprived of a family upbringing and deprived from going near their community for the next 10 to 20 years," he told the ABC.
"No amount of money and no apologies could give that sort of stuff back."