The Atlantic bluefin tuna (hereafter referred to as "bluefin tuna"), one of the world's most valuable and exploited fish species, has been declining in abundance throughout the Atlantic from the 1960s until the mid-2000s. Following the establishment of drastic management measures, the stock has started to recover recently and, as a result, stakeholders have raised catch quotas by 50% for the period 2017-2020. However, stock assessments still omit the natural, long-term variability in the species distribution. Here, we explore the century-scale fluctuations in bluefin tuna abundance and distribution to demonstrate a prevailing influence of the Atlantic Multidecadal Oscillation (AMO) to provide new insights into both the collapse of the Nordic bluefin tuna fishery circa 1963 and the recent increase in bluefin tuna abundance in the Northeast Atlantic. Our results demonstrate how climatic variability can modulate the distribution of a large migrating species to generate rapid changes in its regional abundance, and we argue that climatic variability must not be overlooked in stock management plans for effective conservation.