Mesoscale eddies are ubiquitous features of ocean circulation that modulate the supply of nutrients to the upper sunlit ocean, influencing the rates of carbon fixation and export. The popular eddy-pumping paradigm implies that nutrient fluxes are enhanced in cyclonic eddies because of upwelling inside the eddy, leading to higher phytoplankton production. We show that this view does not hold for a substantial portion of eddies within oceanic subtropical gyres, the largest ecosystems in the ocean. Using space-based measurements and a global biogeochemical model, we demonstrate that during winter when subtropical eddies are most productive, there is increased chlorophyll in anticyclones compared with cyclones in all subtropical gyres (by 3.6 to 16.7% for the five basins). The model suggests that this is a consequence of the modulation of winter mixing by eddies. These results establish a new paradigm for anticyclonic eddies in subtropical gyres and could have important implications for the biological carbon pump and the global carbon cycle.