Understanding the formation and evolution of Cu precipitates in Fe-based alloys is crucial as they are key factors responsible for hardening and embrittlement. Dilute FeCu alloys are model materials for structural components in various application areas, including that of reactor pressure vessel steels for light water nuclear reactors. Positron annihilation spectroscopy (PAS) is a powerful tool to study the nucleation stage of both homogeneous and heterogeneous Cu precipitation, which are beyond the reach of most other experimental techniques. In this work, we present a first-principles study of positron annihilation in Fe -Cu systems. The positron annihilation characteristics (positron lifetimes, Doppler broadening spectra) are calculated for both homogeneous vacancy-free Cu clusters and heterogeneous vacancy-Cu complexes us-ing two-component density functional theory. The theoretical results excellently agree with the available reference PAS experimental results. Our calculations show that the types of Cu precipitates can be clearly distinguished by positron annihilation, and the sizes of Cu precipitates can also be reasonably well es-timated with our calculations. Moreover, we also successfully analyze the evolution of the experimental signals during isochronal annealing where the small Cu clusters change character. This work improves the understanding of the early-stage Cu precipitation in Fe matrix.