A novel theory for the origin of the westward drift of the Earth’s magnetic field is proposed, based upon the propagation of hydrodynamic Rossby waves in the liquid outer core. These waves have the obscure property that their crests always progress eastwards — but for a certain subset, energy can nevertheless be transmitted westwards. In fact, this subset corresponds to sheet-like flow structures, extended in both the axial and radial directions, which are likely to be preferentially excited by convective upwellings in the Earth’s rapidly-rotating outer core. To enable their analysis, the quasi-geostrophic approximation is employed, which assumes horizontal motions to be independent of distance along the rotation axis, yet accounts for variations in the container height (i.e. the slope of the core-mantle boundary). By projecting the momentum equation onto flows of a quasi-geostrophic form, a general equation governing their evolution is derived, which is then adapted for the treatment of two initial value problems – in both Cartesian and spherical geometries – which demonstrate the preference for westward energy propagation by the waves in question. The merits of this mechanism as an explanation for westward drift are discussed.