Edge dislocations are frequently found in epitaxial BiFeO3 multiferroic thin films and are expected to exhibit distinctive and localized magnetoelectric properties. However, an exhaustive characterization of these dislocations at the atomic level has to date been largely overlooked. Here, we use a combination of scanning transmission electron microscopy techniques, atomistic simulations obtained from classical molecular dynamics calculations, and real-space multiple-scattering theory to explore the chemical properties and the bonding characteristics of the atoms located at and near the dislocation cores. We find that in addition to Bi, small amounts of Fe atoms are present in the BiFeO3 dislocation cores which result in uncompensated Fe spins along the dislocations and give rise to a magnetic signal. Our results suggest that edge dislocations in BiFeO3 films could be efficiently used for realizing BiFeO3-based magnetic devices.