Geodetic, seismic, and geological evidence indicates that West Antarctica is underlain by low-viscosity shallow mantle. Thus, as marine-based sectors of the West Antarctic Ice Sheet (WAIS) retreated during past interglacials, or will retreat in the future, exposed bedrock will rebound rapidly and flux meltwater out into the open ocean. Previous studies have suggested that this contribution to global mean sea level (GMSL) rise is small and occurs slowly. We challenge this notion using sea level predictions that incorporate both the outflux mechanism and complex three-dimensional viscoelastic mantle structure. In the case of the last interglacial, where the GMSL contribution from WAIS collapse is often cited as ~3 to 4 meters, the outflux mechanism contributes ~1 meter of additional GMSL change within ~1 thousand years of the collapse. Using a projection of future WAIS collapse, we also demonstrate that the outflux can substantially amplify GMSL rise estimates over the next century.