And the plants, being genetically-modified, would have to undergo rigorous safety checks to ensure they were safe for both public consumption and the environment.
They now hope to develop ways to switch off the gene, producing tea and coffee plants that have the taste of ordinary beverages but do not contain caffeine.
Conventional decaffeination techniques can remove some of the flavour and aromas of drinks.
The researchers say a genetically-modified plant could be the answer, providing all the flavour while being "naturally deficient in caffeine".
Professor Alan Crozier of the University of Glasgow, Scotland, and colleagues in Japan, have cloned the gene encoding "caffeine synthase".
This enzyme catalyses the final steps in the biosynthesis of caffeine in some plants, including the coffee plant Coffea arabica and the tea plant Camellia sinensis.
The research is published in the journal Nature.
'Full-flavour'
Knowing the gene's sequence is the first step towards understanding how it works and then finding ways to inactivate it.
"What cloning the gene means is that it opens up the possibility of using standard molecular biology techniques to make transgenic tea or transgenic coffee that are naturally deficient in caffeine," Professor Crozier told BBC News Online.
"All you are doing is changing one gene and blocking caffeine biosynthesis so it should taste like full-flavoured coffee or tea."
So far, the researchers have only decoded the gene in the laboratory.
Developing decaffeinated tea or coffee plants could take five to 10 years.
And the plants, being genetically-modified, would have to undergo rigorous safety checks to ensure they were safe for both public consumption and the environment.
Some people avoid caffeine, complaining of side effects such as palpitations, indigestion, and insomnia.
At the moment, conventional techniques use chemical solvents or pressurised carbon dioxide to extract the caffeine.
But these techniques can be expensive and can remove some of the flavours and aromas of coffee beans or tea.
And healthy compounds, such as polyphenols in tea, are destroyed in the process.