To understand the dynamics of the Earth’s fluid, iron-rich outer core, only indirect observations are available. The Earth’s magnetic field, originating mainly within the core, and its temporal variations can be used to infer the fluid motion at the top of the core, on a decadal and subdecadal time-scale. Gravity variations resulting from changes in the mass distribution within the Earth may also occur on the same time-scales. Such variations include the signature of the flow inside the core, though they are largely dominated by the water cycle contributions. Our study is based on 8 y of high-resolution, high-accuracy magnetic and gravity satellite data, provided by the CHAMP and GRACE missions. From the newly derived geomagnetic models we have computed the core magnetic field, its temporal variations, and the core flow evolution. From the GRACE CNES/GRGS series of time variable geoid models, we have obtained interannual gravity models by using specifically designed postprocessing techniques. A correlation analysis between the magnetic and gravity series has demonstrated that the interannual changes in the second time derivative of the core magnetic field under a region from the Atlantic to Indian Ocean coincide in phase with changes in the gravity field. The order of magnitude of these changes and proposed correlation are plausible, compatible with a core origin; however, a complete theoretical model remains to be built. Our new results and their broad geophysical significance could be considered when planning new Earth observation space missions and devising more sophisticated Earth’s interior models.