The properties of quantum systems interacting with their environment, commonly called open quantum systems, can be affected strongly by this interaction. Although this can lead to unwanted consequences, such as causing decoherence in qubits used for quantum computation(1), it can also be exploited as a probe of the environment. For example, magnetic resonance imaging is based on the dependence of the spin relaxation times of protons(2) in water molecules in a host's tissue(3). Here we show that the excitation energy of a single spin, which is determined by magnetocrystalline anisotropy and controls its stability and suitability for use in magnetic data-storage devices(4), can be modified by varying the exchange coupling of the spin to a nearby conductive electrode. Using scanning tunnelling microscopy and spectroscopy, we observe variations up to a factor of two of the spin excitation energies of individual atoms as the strength of the spin's coupling to the surrounding electronic bath changes. These observations, combined with calculations, show that exchange coupling can strongly modify the magnetic anisotropy. This system is thus one of the few open quantum systems in which the energy levels, and not just the excited-state lifetimes, can be renormalized controllably. Furthermore, we demonstrate that the magnetocrystalline anisotropy, a property normally determined by the local structure around a spin, can be tuned electronically. These effects may play a significant role in the development of spintronic devices(5) in which an individual magnetic atom or molecule is coupled to conducting leads.