In this work, we investigate the adsorption of a single cobalt atom (Co) on graphene by means of the complete active space self-consistent field approach, additionally corrected by the second-order perturbation theory. The local structure of graphene is modeled by a planar hydrocarbon cluster (C24H12). Systematic treatment of the electron correlations and the possibility to study excited states allow us to reproduce the potential energy curves for different electronic configurations of Co. We find that upon approaching the surface, the ground-state configuration of Co undergoes several transitions, giving rise to two stable states. The first corresponds to the physisorption of the adatom in the high-spin 3d74s2 (S=3/2) configuration, while the second results from the chemical bonding formed by strong orbital hybridization, leading to the low-spin 3d9 (S=1/2) state. Due to the instability of the 3d9 configuration, the adsorption energy of Co is small in both cases and does not exceed 0.35 eV. We analyze the obtained results in terms of a simple model Hamiltonian that involves Coulomb repulsion (U) and exchange coupling (J) parameters for the 3d shell of Co, which we estimate from first-principles calculations. We show that while the exchange interaction remains constant upon adsorption (≃1.1 eV), the Coulomb repulsion significantly reduces for decreasing distances (from 5.3 to 2.6±0.2 eV). The screening of U favors higher occupations of the 3d shell and thus is largely responsible for the interconfigurational transitions of Co. Finally, we discuss the limitations of the approaches that are based on density functional theory with respect to transition metal atoms on graphene, and we conclude that a proper account of the electron correlations is crucial for the description of adsorption in such systems.