Changes in the electronic configuration of iron at high pressures toward a spin-paired state within host minerals ferropericlase and silicate perovskite may directly influence the seismic velocity structure of Earth's lower mantle. We measured the complete elastic tensor of ferropericlase, (Mg(1-x),Fe(x))O (x = 0.06), through the spin transition of iron, whereupon the elastic moduli exhibited up to 25% softening over an extended pressure range from 40 to 60 gigapascals. These results are fully consistent with a simple thermodynamic description of the transition. Examination of previous compression data shows that the magnitude of softening increases with iron content up to at least x = 0.20. Although the spin transition in (Mg,Fe)O is too broad to produce an abrupt seismic discontinuity in the lower mantle, the transition will produce a correlated negative anomaly for both compressional and shear velocities that extends throughout most, if not all, of the lower mantle.