We present the structure of the fully relaxed (001) surface of the half-metallic manganite La_0.7Sr_0.3MnO₃, calculated using density functional theory. Two relevant ferroelastic order parameters are identified and characterized. The known tilting of the oxygen octahedra, which is present in the bulk phase, decreases towards the surface. A ferrodistortive Mn off-centering, triggered by the surface and not reported before, decays monotonically into the bulk. This distortion affects neither the half-metallicity nor the zero-temperature magnetization, but does change the effective spin-spin interactions, and thus the temperature dependence of the magnetic properties.