Marine controlled-source electromagnetic (CSEM) data can be highly sensitive to the presence of resistive hydrocarbon bearing layers in the subsurface. Yet, due to the relatively poor depth resolution of CSEM data and the smoothness constraints imposed by electromagnetic (EM) inversion methods, the resulting resistivity models are often highly smoothed-out, typically underestimating the reservoir resistivity and overestimating its thickness. Conversely, seismic full-waveform inversion (FWI) can accurately recover the depths of seismic velocity changes, yet, is relatively insensitive the presence of hydrocarbons. In spite of their low depth resolution, CSEM data have been shown to be highly sensitive to the resistivity-thickness product of buried resistive layers, suggesting that if the thickness of a target layer can be constrained a priori, very accurate resistivity estimates may be obtained. We developed a method for leveraging the high depth resolution of FWI into a standard CSEM inversion algorithm so that the resulting resistivity models have depth constraints imposed by the seismic structure and consequently may obtain more accurate resistivity estimates. The seismically regularized CSEM inversion that we propose is conceptually similar to minimum-gradient support (MGS) regularization, but it uses regularization weights based on gradients in the seismic velocity model rather than the self-reinforcing model resistivity gradients used in the typical MGS scheme. A suite of synthetic model tests showed how this approach compares with standard smooth and MGS inversions for a range of rock types and hence, levels of correlation between the seismic and resistivity structures, showing that a significantly improved resistivity model can be obtained when the velocity and resistivity profiles are correlated in depth. We also found that this regularization weighting method can be extended to use depth constraints from geophysical data other than seismic velocity models. Tests on a real data example from the Pluto gas field demonstrated how the regularization weights can also be set using a nearby well log, resulting in a more compact estimate of the reservoir resistivity than possible with a standard smooth inversion.