The European summer of 1816 has often been referred to as a 'year without a summer' due to anomalously cold conditions and unusual wetness, which led to widespread famines and agricultural failures. The cause has often been assumed to be the eruption of Mount Tambora in April 1815, however this link has not, until now, been proven. Here we apply state-of-the-art event attribution methods to quantify the contribution by the eruption and random weather variability to this extreme European summer climate anomaly. By selecting analogue summers that have similar sea-level-pressure patterns to that observed in 1816 from both observations and unperturbed climate model simulations, we show that the circulation state can reproduce the precipitation anomaly without external forcing, but can explain only about a quarter of the anomalously cold conditions. We find that in climate models, including the forcing by the Tambora eruption makes the European cold anomaly up to 100 times more likely, while the precipitation anomaly became 1.5-3 times as likely, attributing a large fraction of the observed anomalies to the volcanic forcing. Our study thus demonstrates how linking regional climate anomalies to large-scale circulation is necessary to quantitatively interpret and attribute post-eruption variability.