The origin of Earth's volatiles has been attributed to a late addition of meteoritic material after core-mantle differentiation. The nature and consequences of this 'late veneer' are debated, but may be traced by isotopes of the highly siderophile, or iron-loving, and volatile element selenium. Here we present high-precision selenium isotope data for mantle peridotites, from double spike and hydride generation multi-collector inductively coupled plasma mass spectrometry. These data indicate that the selenium isotopic composition of peridotites is unaffected by petrological processes, such as melt depletion and melt-rock reaction, and thus a narrow range is preserved that is representative of the silicate Earth. We show that selenium isotopes record a signature of late accretion after core formation and that this signature overlaps only with that of the CI-type carbonaceous chondrites. We conclude that these isotopic constraints indicate the late veneer originated from the outer Solar System and was of lower mass than previously estimated. Thus, we suggest a late and highly concentrated delivery of volatiles enabled Earth to become habitable.