Recent discoveries from superconductor (S)/ferromagnet (FM) heterostructures include π-junctions, triplet pairing, critical temperature (Tc) control in FM/S/FM superconducting spin valves (SSVs) and critical current control in S/FM/N/FM/S spin valve Josephson junctions (N: normal metal). In all cases, the magnetic state of the device, generally set by the applied field, controls the superconducting response. We report here the observation of the converse effect, that is, direct superconducting control of the magnetic state in GdN/Nb/GdN SSVs. A model for an antiferromagnetic effective exchange interaction based on the coupling of the superconducting condensation energy to the magnetic state can explain the Nb thickness and temperature dependence of this effect. This superconducting exchange interaction is fundamentally different in origin from the various exchange coupling phenomena that underlie conventional spin electronics (spintronics), and provides a mechanism for the active control of the magnetic state in superconducting spintronics.