<jats:title>Abstract</jats:title><jats:p>Mesoscale ocean eddies, an important element of the climate system, impact ocean circulation, heat uptake, gas exchange, carbon sequestration and nutrient transport. Much of what is known about ongoing changes in ocean eddy activity is based on satellite altimetry; however, the length of the altimetry record is limited, making it difficult to distinguish anthropogenic change from natural variability. Using a climate model that exploits a variable-resolution unstructured mesh in the ocean component to enhance grid resolution in eddy-rich regions, we investigate the long-term response of ocean eddy activity to anthropogenic climate change. Eddy kinetic energy is projected to shift poleward in most eddy-rich regions, to intensify in the Kuroshio Current, Brazil and Malvinas currents and Antarctic Circumpolar Current and to decrease in the Gulf Stream. Modelled changes are linked to elements of the broader climate including Atlantic meridional overturning circulation decline, intensifying Agulhas leakage and shifting Southern Hemisphere westerlies.</jats:p>