Those diagnosed after 25 July 2012 and who cannot sue former employers as they have gone bust or insurance details have disappeared will be eligible.
Ministers said it was a "major breakthrough" to "end an injustice".
Mesothelioma is a fatal disease with average survival rates of about nine months after diagnosis.
It is most prevalent among those who worked in industries with heavy exposure to asbestos up to the 1980s, including construction, shipbuilding, engineering and power generation.
About 2,400 people die every year of the disease and numbers are set to increase over the next 30 years, with an estimated death toll of between 56,000 and 63,000.
While some people have taken legal action to recover damages, many are deterred because of the stress involved. The speed with which the disease takes hold means many die before their cases are heard.
'Peak in cases'
Victims and their families have, up to now, been able to claim damages under two pieces of legislation but the sums paid have not generally exceeded £20,000
.