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Light echoes occur when light from a luminous transient is scattered by dust back into our line of sight with a time delay due to the extra propagation distance. We introduce a novel approach to estimating the distance to a source by combining light echoes with recent three-dimensional dust maps. We identify light echoes from the historical supernovae Cassiopeia A and SN 1572 (Tycho) in nearly a decade of imaging from the All-Sky Automated Survey for Supernovae (ASAS-SN). Using these light echoes, we find distances of $3.6\pm 0.1$kpc and ${3.2}_{-0.2}^{+0.1}$kpc to Cas A and Tycho, respectively, which are generally consistent with previous estimates but are more precise. These distance uncertainties are primarily dominated by the low distance resolution of the 3D dust maps, which will likely improve in the future. The candidate single degenerate explosion donor stars B and G in Tycho are clearly foreground stars. Finally, the inferred reddening towards each SN agrees well with the intervening column density estimates from X-ray analyses of the remnants.