Mr Forrest and his wife Nicola are spearheading a major lobbying campaign to convince federal and state governments to raise the legal tobacco purchase age from 18 to 21 - a move they say would stop young people getting hooked, save lives and save government coffers up to $3.1 billion a year.

Mr Forrest and other members of the Eliminate Cancer Initiative - which the Forrests fund through their philanthropic Minderoo Foundation - have already presented the plan to federal Health Minister Greg Hunt and his state counterparts as part of an all-out assault on big tobacco.

The effort comes after Mr Forrest confirmed last week he is considering suing big tobacco companies for the cost of smoking-related illnesses. The plan is based on a landmark Canadian lawsuit in which three companies were ordered to pay more than $15.6 billion in damages.

Mr Forrest said tobacco companies - which he described as "more cunning than a gold-toothed rat" - must be held accountable for the suffering they have caused Australians. And they cannot be allowed to continue "preying on our vulnerable youth", he said.

"Nearly 90 per cent of adult smokers start as children. By the time they reach 21, they are hooked and become lifelong customers of big tobacco," Mr Forrest said.

"When tobacco causes many times more cost to the nation that it ever brings in revenue, and creates extreme suffering before palliative care and death, there is something seriously wrong with any government in the world, particularly ours, tolerating it."

Dr Ronald DePinho, former president of the MD Anderson Cancer Center in the United States and now an executive director of the ECI, said Australia had an opportunity to inspire the world with "Tobacco 21" legislation.

"Tobacco 21 is a child health issue that must be addressed with urgency, as hundreds of Australian children experiment with tobacco products every day," he said.

Smoking kills an estimated 15,000 Australians every year, and costs taxpayers an estimated $31.5 billion in health and economic costs. These costs dwarf the revenue the Commonwealth reaps in tax revenues from cigarette sales: just over $10 billion in 2016-17.

The "Tobacco 21" plan would save the government $3.1 billion in health and associated economic costs every year, Minderoo modelling has found. Accounting for $1.3 billion in lost tax revenue from cigarette, there would still be a $1.8 billion benefit to Australian taxpayers.

The campaign has the strong backing of the Cancer Council of Australia and the Australian Medical Association.

A March 2015 report by the US-based Institute of Medicine concluded raising the tobacco sale age to 21 would have a substantial positive impact on public health. The change would significantly reduce the number of adolescents and young adults who start smoking and ultimately reduce smoking-related deaths.

The report predicted the change would eventually reduce the smoking rate by about 12 per cent and smoking-related deaths by 10 per cent. In the US, Hawaii and California have recently become the first states to implement Tobacco 21 laws.

The Forrest's helped set up the ECI earlier this year with an initial $75 million in philanthropic funding - part of their record-breaking $400 million donation. It aims to bring the fragmented cancer research community together, accelerate research breakthroughs and improve prevention, detection and treatment, including access to life-saving clinical trials.