The free-space optical communication systems attract significant research and commercial interest the last few years, due to their high performance and reliability characteristics along with their, relatively, low installation and operational cost. Moreover, due to the fact that these systems are using the atmosphere as propagation path, their performance is varying according to its characteristics. Here, we present the performance analysis of a serially relayed radio-on-free-space-optical (RoFSO) communication system which employs the orthogonal frequency division multiplexing technique, with a quadrature amplitude modulation scheme, over atmospheric turbulence channels modelled by either the Gamma-Gamma or the Gamma distribution model. For this RoFSO communication link, we derive closed-form mathematical expressions for the estimation of its average bit error rate and outage probability, taking into account the relays' number, the atmospheric turbulence and the pointing errors effect. Furthermore, for realistic parameter values, numerical results are presented using the derived mathematical expressions, which are verified through the corresponding numerical simulations.