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We present a theoretical study of bound-free electron-positron pair production in the interaction of γ-rays with bare ions. Special attention is paid to the longitudinal polarization of both the emitted positrons and the produced hydrogen-like ions. To evaluate this polarization we employed exact solutions of the relativistic Dirac equation and treat the electron-photon coupling within the framework of first-order perturbation theory. Detailed calculations have been performed for both, low-and high-Z ions and for a wide range of photon energies. The results of these calculations suggest that bound-free pair production can be a source of strongly polarized positrons and ions.