Health Minister Greg Hunt and ACT senator Zed Seselja will on Thursday announce the Commonwealth's support for the landmark program, declaring it is the "right thing to do".

The ACT, which will establish and administer the fund, will match the federal government's contribution.

The two Morrison government ministers have credited the "tireless" advocacy of mesothelioma sufferer James Wallner, who has been lobbying the federal government to support victims after he was diagnosed with the incurable disease in July last year.

Mr Wallner's wife, Linda, welcomed the announcement on behalf of the family.

"All things considered, it is worthwhile celebrating. As a family, we are really grateful for the scheme," she said.

"I do think that if this had been present 10 months ago, it would have taken away a small amount of suffering."

Ms Wallner said her husband was now in an "end-of-life stage" after his condition deteriorated over recent weeks.

ACT Chief Minister Andrew Barr last year announced plans to set up a financial assistance scheme for people who contracted mesothelioma after living in a Mr Fluffy home, after his government agreed to cover up to $250,000 worth of Mr Wallner's medical expenses.

Mr Barr said at the time that he would lobby the federal government to cover the costs of the scheme.

Mr Wallner's family made an impassioned plea to Mr Hunt soon after the diagnoses, imploring the Commonwealth to finally take responsibility for a problem born while the ACT was under its control.

"Minister, it is time for you to mend this gap," Mr Wallner's brother wrote in the letter.

"If you don't, I can only conclude that you are content to sit by and watch as my brother, and those that will follow him, die without being able to afford the necessary life-prolonging medical treatments now available."

Mr Hunt initially rebuffed the family's request, arguing support for Mr Fluffy victims was a territory responsibility.

But he continued to face pressure, including from ACT Senator Zed Seselja, who suggested the Commonwealth partner with the ACT to manage the health impacts of the crisis, as it did with the Mr Fluffy buyback and demolition scheme in 2014.

Mr Hunt earlier this year reportedly wrote to Mr Wallner's family and friends to inform them that the government was now actively pursuing a new scheme for Mr Fluffy victims.

It has now agreed to help fund the ACT's scheme.

"I have been deeply moved by the suffering of those who have developed mesothelioma and other asbestos related illnesses, through the simple act of living in their home," Mr Hunt said.

Senator Seselja said the federal government's contributing to the scheme was the "right thing to do".

"I have heard the heartbreaking stories of Canberrans who have suffered greatly as a result of living in a Mr Fluffy home. I hope that in some small way this scheme can ease the burden they and their loved ones face," he said.

While full details of the scheme will be announced in the coming weeks, Mr Barr said it would exist to support people who might contract mesothelioma because of historic exposure to a Mr Fluffy homes, including with medical expenses.

Mr Barr welcomed the federal government's contribution, which he said recognised the joint responsibility to help sufferers.

"While the remediation process to remove Mr Fluffy affected homes once and for all has been successful, we may see more Canberrans suffer the harshest impacts of exposure to loose fill asbestos in the home," he said.

"This scheme is an important next step in the government's future response to the legacy of Mr Fluffy.

"The loose fill asbestos was installed in these households before self-government, and the original response was conducted by the Commonwealth government."

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