We investigate the adsorption of a Ni monolayer on the β-SiC(001) surface by means of highly precise first-principles all-electron FLAPW calculations. Total energy calculations for the Si- and C-terminated surfaces reveal high Ni adsorption energies, with respect to other metals, confirming the strong reactivity and the stability of the transition metal/SiC interface. These high binding energies, about 7.3-7.4 eV, are shown to be related to strong p-d hybridization, common to both surface terminations and different adsorption sites, which, despite the large mismatch, may stabilize overlayer growth. A detailed analysis of the bonding mechanism, in terms of density of states and hybridization of the surface states, reveals the strong covalent character of the bonding. We also calculate and discuss the Schottky barrier heights at the Ni/SiC junction for both terminations.