Mr Lennon says he will introduce legislation by the end of next month to compensate Aborigines forcibly removed from their families.
"This fundamental has to be addressed before we can achieve true reconciliation with the Tasmanian Aboriginal people," he said.
Tasmania's Aboriginal Legal Centre spokesman Michael Mansell estimates that at least 40 Aborigines will have a case for compensation, which he hopes will be in the vicinity of $100,000 per person.
Mr Lennon would not confirm a dollar value, but said he was confident the legislation would deal with the stolen generations in a way that was "acceptable" to Tasmanian Aborigines and the wider community.
If passed Mr Lennon says the legislation will send "a very powerful message to the rest of Australia about what needs to be done if we're to advance Aboriginal reconciliation".