Neutron-rich material ejected from neutron star-neutron star (NS-NS) and neutron star-black-hole (NS-BH) binary mergers is heated by nuclear processes to temperatures of a few hundred keV, resulting in a population of electron-positron pairs. Some of the positrons escape from the outer layers of the ejecta. We show that the population of low-energy positrons produced by NS-NS and NS-BH mergers in the Milky Way can account for the observed 511-keV line from the Galactic center (GC). Moreover, we suggest how positrons and the associated 511-keV emission can be used as tracers of recent mergers. Recent discovery of 511-keV emission from the ultrafaint dwarf galaxy Reticulum II, consistent with a rare NS-NS merger event, provides a smoking-gun signature of our proposal.