The strong parallels between coordination chemistry and adsorption on metal surfaces, with molecules and ligands forming local bonds to individual atoms within a metal surface, have been established over many years of study. The recently proposed "surface trans-effect" (STE) appears to be a further manifestation of this analogous behaviour, but so far the true nature of the modified molecule-metal surface bonding has been unclear. The STE could play an important role in determining the reactivities of surface-supported metal-organic complexes, influencing the design of systems for future applications. However, the current understanding of this effect is incomplete and lacks reliable structural parameters with which to benchmark theoretical calculations. Using X-ray standing waves, we demonstrate that ligation of ammonia and water to iron phthalocyanine (FePc) on Ag(111) increases the adsorption height of the central Fe atom; dispersion corrected density functional theory calculations accurately model this structural effect. The calculated charge redistribution in the FePc/H2O electronic structure induced by adsorption shows an accumulation of charge along the σ-bonding direction between the surface, the Fe atom and the water molecule, similar to the redistribution caused by ammonia. This apparent σ-donor nature of the observed STE on Ag(111) is shown to involve bonding to the delocalised metal surface electrons rather than local bonding to one or more surface atoms, thus indicating that this is a true surface trans-effect.