Debris flows are concentrated slurries of water and sediment that shape the landscape and pose a major hazard to human life and infrastructure. Seismic ground motion-based observations promise to provide new, remote constraints on debris flow physics, but the lack of data and a theoretical basis for interpreting them hinders progress. Here we present a new mechanistic physical model for the seismic ground motion of debris flows. We find that the amplitude and frequency characteristics of the seismic data can distinguish debris flows from other seismic sources. The model suggests that seismic ground motion amplitudes are most sensitive to the product of physical parameters related to the debris flow: average flow speed, length and width of boulder snout, and boulder sizes. The model also implies that peak frequency of the seismic signal depends on average distance of the debris flow from the instrument. Applying the modeling framework to the Montecito debris flows, California on 9 January 2018, we can determine that the average distance to the nearest debris flows and that the estimated grain sizes and flow speeds are consistent with observations. The ability to accurately describe the absolute seismic amplitude of debris flow source is a key step towards creating a physics-based early warning system for this particular natural hazard.