The Eldgjá lava flood is considered Iceland's largest volcanic eruption of the Common Era. While it is well established that it occurred after the Settlement of Iceland (circa 874 CE), the date of this great event has remained uncertain. This has hampered investigation of the eruption's impacts, if any, on climate and society. Here, we use high-temporal resolution glaciochemical records from Greenland to show that the eruption began in spring 939 CE and continued, at least episodically, until at least autumn 940 CE. Contemporary chronicles identify the spread of a remarkable haze in 939 CE, and tree ring-based reconstructions reveal pronounced northern hemisphere summer cooling in 940 CE, consistent with the eruption's high yield of sulphur to the atmosphere. Consecutive severe winters and privations may also be associated with climatic effects of the volcanic aerosol veil. Iceland's formal conversion to Christianity dates to 999/1000 CE, within two generations or so of the Eldgjá eruption. The end of the pagan pantheon is foretold in Iceland's renowned medieval poem, Vǫluspá ('the prophecy of the seeress'). Several lines of the poem describe dramatic eruptive activity and attendant meteorological effects in an allusion to the fiery terminus of the pagan gods. We suggest that they draw on first-hand experiences of the Eldgjá eruption and that this retrospection of harrowing volcanic events in the poem was intentional, with the purpose of stimulating Iceland's Christianisation over the latter half of the tenth century.