The leaders made their appeal ahead of a G-7 summit in Britain which begins on Friday, when United States President Joe Biden will meet the leaders of Britain, France, Germany, Italy, Canada and Japan.
In their letter to the G-7, the former world leaders said global cooperation had failed in 2020, but that 2021 could usher in a new era.
"Support from the G-7 and G-20 that makes vaccines readily accessible to low- and middle-income countries is not an act of charity, but rather is in every country's strategic interest," the letter said, Reuters reported.
Among the signatories were former British premiers Gordon Brown and Tony Blair, former United Nations secretary-general Ban-Ki Moon and 15 former African leaders.
They said the G-7 and other leaders invited to the summit should guarantee to pay what would amount to about US$30 billion (S$39.72 billion) a year over two years towards fighting the pandemic worldwide.
"For the G-7 to pay is not charity, it is self-protection to stop the disease spreading, mutating and returning to threaten all of us," Brown said.
"Costing just 30 pence (56 Singapore cents) per person per week in Britain, it is a small price to pay for the best insurance policy in the world," he added in a statement.
Their plea coincided with a poll by the Save the Children charity which found strong public support in the US, Britain, France, Germany and Canada for the G-7 paying towards the US$66 billion needed for COVID-19 vaccines globally.
In Britain, 79 per cent were in favor of such a policy, while 79 per cent of Americans backed the proposal, the poll showed. Support was lowest in France, where 63 per cent were in favor.