The leaders made their appeal ahead of a G7 summit in England which begins on Friday, when US President Joe Biden will meet the leaders of Britain, France, Germany, Italy, Canada and Japan.
In their letter to the G7, the former world leaders said global cooperation had failed in 2020, but that 2021 could usher in a new era.
"Support from the G7 and G20 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.
Among the signatories were ex-British premiers Gordon Brown and Tony Blair, former U.N. Secretary General Ban-Ki Moon and 15 former African leaders.
They said the G7 and other leaders invited to the summit should guarantee to pay what would amount to about US$30 billion a year over two years towards fighting the pandemic worldwide.
"For the G7 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 (US$0.43) per person per week in the UK, is a small price to pay a 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 United States, Britain, France, Germany and Canada for the G7 paying towards the US$66 billion needed for COVID-19 vaccines globally.
In Britain, 79% were in favour of such a policy, while 79% of Americans backed the proposal, the poll showed. Support was lowest in France, where 63% were in favour.