In this paper, we develop a novel moment-based approach for the evaluation of the outage probability (OP) in a generalized fading environment with interference and noise. Our method is based on the derivation of a power series expansion of the OP of the signal-to-interference-plus-noise ratio (SINR). It does not necessitate stringent requirements, the only major ones being the existence of a power series expansion of the cumulative distribution function of the desired user power and the knowledge of the cross-moments of the interferers’ powers. The newly derived formula is shown to be applicable for most of the well-practical fading models of the desired user under some assumptions on the parameters of the powers’ distributions. A further advantage of our method is that it is applicable irrespective of the nature of the fading models of the interfering powers, the only requirement being the perfect knowledge of their crossmoments. In order to illustrate the wide scope of applicability of our technique, we present a convergence study of the provided formula for the Generalized Gamma and the Rice fading models. Moreover, we show that our analysis has direct bearing on recent multi-channel applications using selection diversity techniques. Finally, we assess by simulations the accuracy of the proposed formula for various fading environments.