The F composite fading model was recently proposed as an accurate and tractable statistical model for the characterization of the simultaneous occurrence of multipath fading and shadowing conditions encountered in realistic wireless communication scenarios. In the present contribution we capitalize on the distinct properties of this composite model to derive the achievable capacity over F composite fading channels assuming fixed rate quality of service requirements. To this end, novel exact and tractable analytic expressions are derived for both the exact and the truncated channel inversion strategies. This also enables the derivation of additional simplified approximate and asymptotic expressions for these cases, which provide meaningful insights on the effect of fading conditions on the overall system performance. This is particularly useful in the context of numerous emerging wireless applications of interest that exhibit stringent fixed rate requirements such as vehicular communications, body area networks and telemedicine, among others.