The excess of highly siderophile elements in the Earth's mantle is thought to reflect the addition of primitive meteoritic material after core formation ceased(1-4). This 'late veneer' either comprises material remaining in the terrestrial planet region after the main stages of the Earth's accretion(5,6), or derives from more distant asteroidal(7) or cometary(8) sources. Distinguishing between these disparate origins is important because a late veneer consisting of carbonaceous chondrite-like asteroids(7) or comets(8) could be the principal source of the Earth's volatiles and water. Until now, however, a 'genetic' link between the late veneer and such volatile-rich materials has not been established or ruled out. Such genetic links can be determined using ruthenium (Ru) isotopes, because the Ru in the Earth's mantle predominantly derives from the late veneer(9), and because meteorites exhibit Ru isotope variations arising from the heterogeneous distribution of stellar-derived dust(10,11). Although Ru isotopic data and the correlation of Ru and molybdenum (Mo) isotope anomalies in meteorites were previously used to argue that the late veneer derives from the same type of inner Solar System material as do Earth's main building blocks(6), the Ru isotopic composition of carbonaceous chondrites has not been determined sufficiently well to rule them out as a source of the late veneer. Here we show that all chondrites, including carbonaceous chondrites, have Ru isotopic compositions distinct from that of the Earth's mantle. The Ru isotope anomalies increase from enstatite to ordinary to carbonaceous chondrites, demonstrating that material formed at greater heliocentric distance contains larger Ru isotope anomalies. Therefore, these data refute an outer Solar System origin for the late veneer and imply that the late veneer was not the primary source of volatiles and water on the Earth.