In this letter, the outage performance of a satellite-assisted cooperative non-orthogonal multiple access (NOMA) system is studied, where a terrestrial source communicates with one terrestrial destination directly while the other terrestrial destination is assisted by a regenerative satellite. We consider the satellite channels and the terrestrial channels undergo shadowed-Rician fading and Nakagami- $m$ fading, respectively. Based on this, we derive the exact closed-form expressions for the outage probabilities. In addition, the asymptotic expressions at high signal-to-noise ratio are provided to gain further insights. Simulation results validate the accuracy of the analytical results and show the superiority over other conventional schemes.