The anomalous magnetic moments of the baryon octet are calculated in broken SU(3) symmetry using low-energy pole dominance as a dynamical model and keeping only the lowest lying intermediate states, the psuedoscalar-meson-baryon states. By using dispersion theory, the anomalous moments are related to an energy integral over the S12 and P12 photomeson production amplitudes, which at low energy and for vanishing meson mass are exactly given by the pole terms. From this exact information we calculate the low-energy contribution to the anomalous moments, keeping all orders in baryon and meson mass splittings and using the SU(3)-symmetric strong-coupling constants. We are able to account for the dominant contribution to the proton and neutron magnetic moment and find in addition, for an FD ratio~0.6, that K(Λ)~0.4K(n), in agreement with the observed value. The SU(3) predictions for the other moments and the Σ0-->Λ+γ transition moment are found to be more badly violated.