The structural, electronic and magnetic (including magnetic anisotropy) properties of the Co/Pd(111) and Co/Pt(111) systems were investigated using the local density total energy full potential linearized augmented plane wave (FLAPW) method. Structurally, the pseudomorphic Co overlayer occupies the fcc sites on the substrates, with a 5-6% contraction of nearest Co-Pd and Co-Pt distances. As results of a second variation magnetic anisotropy calculation, Co/Pt(111) shows strong perpendicular spin orientation (with an anisotropy energy approximately 4.5 X 10(-4) eV/adatom). Strong covalent overlayer/substrate bonding results in large adsorption energies of 2.2-2.5 eV/adatom. Unlike other magnetic/nonmagnetic adsorption systems, Co atoms retain (or even enhance) their local magnetic moment as in the free-standing Co monolayer. The Co overlayer induces a long-range (beyond 3 atomic layers) spin polarization in Pd(111), but a relatively shorter-range disturbance in Pt(111).