Scotland's Parliament overturned a House of Lords ruling that people diagnosed with pleural plaques cannot claim damages.
The law was passed at Holyrood with a 98-16 majority despite Tory opposition.
The insurance industry have continually argued that pleural plaques themselves are not harmful and should not offer sufferers a route to compensation.
The ABI, Association of British Insurers claim that over the next 20 years the costs will average between £76 million and £607 million, the Governement estmate between £7 million and £19 million.
Labour justice spokesman Richard Baker said the case to allow claims was "irrefutable".
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