To date, scientists have tried to count distinct lines in the vertebrae of dead whale sharks. These act like rings in a tree trunk, increasing as the animal gets older.
But they have been unsure about how often these rings can form and the reasons behind them.
Now researchers say they have come up with a much more accurate way of determining the whale sharks' true age.
From the late 1940s, several nations including the US, the Soviet Union, Great Britain, France and China conducted atomic bomb tests in different locations.
One side effect of all these explosions was the doubling of an atom type, or isotope, called Carbon-14 in the atmosphere.
Over time, every living thing on the planet has absorbed this extra Carbon-14 which still persists.
But as scientists know the rate at which this isotope decays, it is a very useful marker in determining age.
The older the creature, the less Carbon-14 you'd expect to find.
This team managed to find two long-dead specimens stored in Pakistan and Taiwan.
"The absolute longevity of these animals could be very, very old, possibly as much as 100-150 years old," said Dr Meekan.
"This has huge implications for the species. It suggests that these things are probably intensely vulnerable to over-harvesting."
The scientists say their results explain why whale shark numbers have collapsed in locations like Thailand and Taiwan where fishing has taken place.
"They are just not built for humans to exploit," said Dr Meekan.
In many tropical regions, whale shark tourism is now a major attraction. The researchers say that encouraging co-operation between different countries along the vast routes that whale sharks follow is key to their survival.
"Whale sharks are a fantastic ambassador for marine life and one that has lifted so many people out of poverty," added Dr Meekan.
