High-density microelectrode arrays (MEAs) have opened new possibilities for systems neuroscience in human and non-human animals, but brain tissue motion relative to the array poses a challenge for downstream analyses, particularly in human recordings. We introduce DREDge (Decentralized Registration of Electrophysiology Data), a robust algorithm which is well suited for the registration of noisy, nonstationary extracellular electrophysiology recordings. In addition to estimating motion from spikes in the action potential (AP) frequency band, DREDge enables automated tracking of motion at high temporal resolution in the local field potential (LFP) frequency band. In human intraoperative recordings, which often feature fast (period <1s) motion, DREDge correction in the LFP band enabled reliable recovery of evoked potentials, and significantly reduced single-unit spike shape variability and spike sorting error. Applying DREDge to recordings made during deep probe insertions in nonhuman primates demonstrated the possibility of tracking probe motion of centimeters across several brain regions while simultaneously mapping single unit electrophysiological features. DREDge reliably delivered improved motion correction in acute mouse recordings, especially in those made with an recent ultra-high density probe. We also implemented a procedure for applying DREDge to recordings made across tens of days in chronic implantations in mice, reliably yielding stable motion tracking despite changes in neural activity across experimental sessions. Together, these advances enable automated, scalable registration of electrophysiological data across multiple species, probe types, and drift cases, providing a stable foundation for downstream scientific analyses of these rich datasets.