The ruling prevented compensation claims for pleural plaques, a scarring of the lungs, arguing that it was technically not a disease.
Scottish Justice Secretary Kenny MacAskill said the condition increased risk of diseases like mesothelioma.
The SNP government is to bring forward a Holyrood bill to make the changes.
Health issues in Scotland are devolved to Holyrood and Mr MacAskill said there was sufficient concern about pleural plaques to warrant legislation.
The planned measures, which would take effect from the date of the Lords judgment on 17 October, would mean that those negligently exposed to asbestos who were diagnosed with pleural plaques would continue to be able to raise an action for damages.
"The effects of asbestos are a terrible legacy of Scotland's industrial past and we should not turn our backs on those who contributed to our nation's wealth in the past," said Mr MacAskill.
"Pleural plaques in anyone exposed to asbestos mean they have a greatly increased lifetime risk of developing mesothelioma and a small but significantly increased risk of developing bronchial carcinoma."
Pleural plaques - small areas of benign scarring on the lungs - are an indicator of exposure to asbestos and Law Lords had ruled that it should not be open to compensation claims because it was not a disease and had no symptoms.
Although pleural plaques do not cause or develop into a more serious asbestos-related condition, they do signify an increased risk of developing mesothelioma because of exposure to asbestos.
Serious respiratory diseases, including mesothelioma and lung cancer, have been diagnosed in hundreds of men in Scotland - most of them former Clydeside shipyard workers.
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