The accretion of volatile-rich material from the outer Solar System represents a crucial prerequisite for Earth to develop oceans and become a habitable planet(1-4). However, the timing of this accretion remains controversial(5-8). It has been proposed that volatile elements were added to Earth by the late accretion of a late veneer consisting of carbonaceous-chondrite-like material after core formation had ceased(6,9,10). This view could not be reconciled with the ruthenium (Ru) isotope composition of carbonaceous chondrites(5,11), which is distinct from that of the modern mantle(12), or of any known meteorite group(5). As a possible solution, Earth's pre-late-veneer mantle could already have contained a fraction of Ru that was not fully extracted by core formation(13). The presence of such pre-late-veneer Ru can only be established if its isotope composition is distinct from that of the modern mantle. Here we report the first high-precision, mass-independent Ru isotope compositions for Eoarchaean ultramafic rocks from southwest Greenland, which display a relative Ru-100 excess of 22 parts per million compared with the modern mantle value. This Ru-100 excess indicates that the source of the Eoarchaean rocks already contained a substantial fraction of Ru before the accretion of the late veneer. By 3.7 billion years ago, the mantle beneath southwest Greenland had not yet fully equilibrated with late accreted material. Otherwise, no Ru isotopic difference relative to the modern mantle would be observed. If constraints from other highly siderophile elements besides Ru are also considered(14), the composition of the modern mantle can only be reconciled if the late veneer contained substantial amounts of carbonaceous-chondrite-like materials with their characteristic Ru-100 deficits. These data therefore relax previous constraints on the late veneer and are consistent with volatile-rich material from the outer Solar System being delivered to Earth during late accretion.