The F composite fading model was recently proposed as an accurate and tractable statistical model for the characterization of the composite fading conditions encountered in realistic wireless communication scenarios. In the present contribution we capitalize on the distinct properties of this composite model to evaluate the achievable ergodic capacity over F composite fading channels. To this end, we derive an exact closed-form expression for the ergodic capacity, which is subsequently used as a benchmark for the derivation of a tight approximation and a particularly accurate asymptotic representation for large average signal-to-noise ratio values. The derived analytic expressions are provided in closed-form and benefit from their analytical and numerical tractability. This enables the development of meaningful insights on the effect of fading conditions of different severity levels on the overall system performance. Also, it allows the accurate quantification of the signal to noise ratio required in target quality of service requirements under different composite fading conditions.