A combination of density functional theory calculations, many-body model considerations, and magnetization and electron-spin-resonance measurements shows that the multiferroic FeTe2O5Br should be described as a system of alternating antiferromagnetic S = 5/2 chains with strong Fe-O-Te-O-Fe bridges weakly coupled by two-dimensional frustrated interactions, rather than the previously reported tetramer model. The peculiar temperature dependence of the incommensurate magnetic vector can be explained in terms of interchain exchange striction being responsible for the emergent net electric polarization.