Tsunami wave observations far from the coast remain challenging due to the logistics and cost of deploying and operating offshore instrumentation on a long-term basis with sufficient spatial coverage and density. Distributed Acoustic Sensing (DAS) on submarine fiber optic cables now enables real-time seafloor strain observations over distances exceeding 100 km at a relatively low cost. Here, we evaluate the potential contribution of DAS to tsunami warning by assessing theoretically the sensitivity required by a DAS instrument to record tsunami waves. Our analysis includes signals due to two effects induced by the hydrostatic pressure perturbations arising from tsunami waves: the Poisson’s effect of the submarine cable and the compliance effect of the seafloor. It also includes the effect of seafloor shear stresses and temperature transients induced by the horizontal fluid flow associated with tsunami waves. The analysis is supported by fully coupled 3-D physics-based simulations of earthquake rupture, seismo-acoustic waves and tsunami wave propagation. The strains from seismo-acoustic waves and static deformation near the earthquake source are orders of magnitude larger than the tsunami strain signal. We illustrate a data processing procedure to discern the tsunami signal. With enhanced low-frequency sensitivity on DAS interrogators (strain sensitivity ≈ 2×10−10 at mHz frequencies), we find that, on seafloor cables located above or near the earthquake source area, tsunamis are expected to be observable with a sufficient signal-to-noise ratio within a few minutes of the earthquake onset. These encouraging results pave the way towards faster tsunami warning enabled by seafloor DAS.