The origin of volatiles in the Moon's interior is debated. Scenarios range from inheritance through a Moon-forming disk or "synestia" to late accretion by meteorites or comets. Noble gases are excellent tracers of volatile origins. We report analyses of all noble gases in paired, unbrecciated lunar mare basalts and show that magmatic glasses therein contain indigenous noble gases including solar-type He and Ne. Assimilation of solar wind (SW)-bearing regolith by the basaltic melt or SW implantation into the basalts is excluded on the basis of the petrological context of the samples, as well as the lack of SW and "excess 40Ar" in the magmatic minerals. The absence of chondritic primordial He and Ne signatures excludes exogenous contamination. We thus conclude that the Moon inherited indigenous noble gases from Earth's mantle by the Moon-forming impact and propose storage in the incompatible element-enriched ("KREEP") reservoir.