Thousands of patients, or their families, will be able to apply to the £380m pot from next month.
Those diagnosed after July 2012 and who cannot sue former employers as they have gone bust or insurance details have disappeared will be eligible.
Ministers said the move ended "years of injustice".
Mesothelioma can take decades to develop, but when symptoms emerge it progresses rapidly.
Most die within three years of being diagnosed.
Around 2,000 people are diagnosed each year, and the numbers are set to increase over the next 30 years, with an estimated death toll of between 56,000 and 63,000, according to the Department for Work and Pensions.
The cancer 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.
Until now, victims and their families have been able to claim damages under two pieces of legislation but the sums paid have not generally exceeded £20,000.
The new fund will entitle UK claimants to 80% of the average settlement paid out in civil actions relating to mesothelioma, meaning payments will range from £115,000 to £123,000.
On top of the payment, the fund will pay out £7,000 towards legal costs.
The Mesothelioma Act was passed in January and allowed the creation of the compensation pot, funded by the insurance industry.
Those diagnosed before the scheme was first announced, on 25 July 2012, will not be eligible.
Claimants will have to demonstrate that they were negligently exposed to asbestos at work and are unable to claim compensation because they cannot track down a liable employer or insurer.
Work and Pensions Minister Mike Penning said: "This will end years of injustice for mesothelioma victims and their families - who have had to endure this terrible disease with little hope of any compensation from the insurance industry.
"We have made it an absolute priority to bring in the scheme as soon as legislation will allow, so I am pleased to announce that victims will be able to apply for payments from next month."
According to government calculations, around 3,500 patients or their dependants are likely to be eligible for support.
Dr John Moore-Gillon, honorary medical adviser at the British Lung Foundation, said: "Mesothelioma is a particularly devastating disease, killing over 2,400 people every year in the UK, most of whom were innocently exposed to asbestos in the work place.
"The government's announcement today is therefore a positive move for mesothelioma patients and their families, many of whom struggled to gain any compensation at all until recently.
"What we urgently need to see now is greater commitment to funding research into new treatments for mesothelioma."
He added: "Although compensation awards are very helpful, they don't change the fact that most people who develop mesothelioma will be dead in less than three years.
"Only research investment will change that - it is what patients and their families want, and with over 50,000 likely to die of the disease in the UK within the next 30 years, it is something we desperately need to prioritise."
Victims of mesothelioma, an aggressive cancer caused by exposure to asbestos, are to receive an average of £123,000 compensation from a new fund.