The 1257 eruption was so large it left its chemical signature in the ice of both the arctic and the antarctic, they said.
Writing in the PNAS journal, an international team has named the Samalas Volcano on Lombok Island, Indonesia, as the culprit.
"The evidence is very strong and compelling," Clive Oppenheimer of Britain's Cambridge University told the BBC.
A huge crater lake now occupies what it left of the original mountainous structure of the volcano, researchers said.
Franck Lavigne of the Pantheon-Sorbonne University in France said the research was conducted similar to a criminal investigation.
"We didn't know the culprit at first, but we had the time of the murder and the fingerprints in the form of the geochemistry in the ice cores, and that allowed us to track down the volcano responsible," he said.
Volcanoes in Mexico, Ecuador and New Zealand had been suggested as sources of the eruption but all fail on their dating or geochemistry, the researchers said.
Only Samalas matches all the evidence, they said.
The researchers estimate the eruption hurled 10 cubic miles of rock and ash into the atmosphere to a height of 25 miles or more, with a significant impact on global climate.