The microscopic theory of the magnetically anisotropic effective pseudo-spin-1/2 Hamiltonian for a pair of Co2+ ions is reported. In the framework of the second-order perturbation approach, the analytical expressions are found for the components of the tensor of the exchange interaction, g-tensor, and the factor in the temperature independent paramagnetic contribution. The parameters of the Hamiltonian are expressed in terms of the basic intra- and intercenter parameters of the pair, namely, the spin-orbit coupling constant, orbital reduction factor, exchange integral, and low symmetry crystal field parameters including axial and rhombic terms.