But the approval has not been extended to his daughter Marrakech Jennings-Lowry for the disorders of her heart, lungs and other conditions which the family blame on her father's Agent Orange exposure.
The Otago University study by Associate Professor David McBride and colleagues, to be published in the British medical journal BMJ Open, compares 1998-2008 cancer and death rates of more than 2700 men who served in Vietnam, with rates for the general population.
The former servicemen have had acute lymphatic leukaemia at nearly twice the national rate. Their death rates for cancers of the head, neck, mouth and throat have been more than twice the national rate.
The New Zealand veterans may also have had a 6 per cent greater incidence of all cancers, but the study was too small to be sure, unlike a much larger study of Australia's Vietnam veterans, which found an increase of 15 per cent.
Chronic lymphatic leukaemia was among four types of cancer and a skin condition listed by the Government in 2006 as conditions for which sufferers who had served in Vietnam would qualify for ex gratia payments under a $30 million compensation package.
Those five diseases are joined by 10 others - including prostate cancer, Parkinson's disease, coronary heart disease and peripheral nerve disease - on a Veterans' Affairs NZ list for conditions "presumed to be attributable to service" in Vietnam.
Veterans diagnosed with one of the conditions are entitled to a war disablement pension.
Vietnam Veterans Association president John Deazley said the New Zealand study, the first of its kind, was long overdue.
"We are very happy that it has been done in New Zealand for New Zealanders because it brings us in line with the studies that have been done in Australia, with whom the majority of the New Zealanders served."
The Otago and Australian studies found the death rate from all causes was lower for the veterans than the general population. This is attributed to "healthy soldier effect", the armed services' health screening of recruits leading to a healthier-than-average group of people.
The link
* Defoliant herbicide Agent Orange contained toxic dioxin.
* There is "sufficient'' evidence that past exposure to it is linked to an increased risk of developing some cancers, including chronic lymphatic leukaemia.
* New Zealand Vietnam War veterans have nearly twice the rate of that type of cancer, compared with the national population.