Starting with the double generalized Gamma (GG) model to describe turbulence-induced fading in free-space optical (FSO) systems, we propose a new unified model that accounts for the impact of pointing errors and type of receiver detector. More specifically, we present unified closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-toend signal-to-noise ratio (SNR) of a single link FSO transmission system in terms of the Meijer’s G-function. We then use these unified expressions to evaluate performance measures such as the bit error rate, the outage probability, and the ergodic capacity of (i) a single FSO link operating over double GG fading model (ii) asymmetric RF-FSO dual-hop relay transmission system with fixed gain relay. Using an asymptotic expansion of the Meijer’s G-function at high SNR, we express all the expressions, derived earlier, in terms of elementary functions. All our analytical results are verified using computer based Monte-Carlo simulations.