The House of Lords ruling prevented workers from making compensation claims for pleural plaques, a scarring of the lungs, arguing that it was technically not a disease.
The local MSP had tabled a parliamentary question pressing the Government to introduce a Bill to allow those diagnosed with pleural plaques to make a claim for compensation.
Ms Jamieson said: "Workers who have been negligently exposed to asbestos and who have been diagnosed with pleural plaques must have the right to raise an action for damages. A diagnosis of pleural plaques can mean a significantly increased risk of developing deadly asbestos-related conditions such as mesothelioma and bronchial carcinoma.
"The Scottish Government must act quickly to give Scottish workers the right to claim compensation and I have been given an assurance that legislation will be introduced before the summer."