The average intercalation voltages (AIV) of cathode materials for rechargeable lithium-ion batteries are calculated from first principles using the LAPW method for both trigonal layered (LiMO2) and cubic spinel (LiM2O4) structures. All calculated AIV are in good agreement with corresponding plateaus of measured open circuit voltages. It is shown that the AIV is directly related to the change of bonding occurring upon the intercalation of lithium. With increasing atomic number of the transition metal up to Co the increase of the AIV is caused by the increase in Li-O stabilizing interaction, which in turn is induced by increasing covalency of M-O bonding. The AIV is demonstrated not to depend on the structure but only on the oxidation state of the transition metal.