The sub-seasonal variability of the extra-tropical large-scale atmospheric flow is characterized by recurrent or quasi-stationary circulation anomalies, termed weather regimes. Despite the usefulness of these regimes in numerous meteorological and socioeconomic applications, there is an ongoing debate as to whether they represent physical modes of the atmosphere, or are merely useful statistical categorizations. Here, we answer this question for wintertime Atlantic-European regimes. We argue that dynamical systems theory applied to a refined regime definition provides strong evidence in support of most weather regimes being physically meaningful. This finding underpins the broad relevance of weather regimes, for understanding the response of the atmosphere to external forcing, supporting sub-seasonal weather forecasting, and down-scaling of climate projections.