Using density-functional calculations, we study the effect of sp3-type defects created by different covalent functionalizations on the electronic and magnetic properties of graphene. We find that the induced magnetic properties are universal, in the sense that they are largely independent of the particular adsorbates considered. When a weakly polar single covalent bond is established with the layer, a local spin moment of 1.0 μB always appears in graphene. This effect is similar to that of H adsorption, which saturates one pz orbital in the carbon layer. The magnetic couplings between the adsorbates show a strong dependence on the graphene sublattice of chemisorption. Molecules adsorbed at the same sublattice couple ferromagnetically, with an exchange interaction that decays very slowly with distance, while no magnetism is found for adsorbates at opposite sublattices. Similar magnetic properties are obtained if several pz orbitals are saturated simultaneously by the adsorption of a large molecule. These results might open new routes to engineering the magnetic properties of graphene derivatives by chemical means.