The aim of this work is the formulation and derivation of the η-μ/Inverse Gaussian composite distribution which corresponds to a physical fading model. The η-μ distribution is a generalized small-scale fading model which accounts effectively for non-line-of-sight scenarios and includes as special cases the widely known Nakagami-m, Rayleigh, Hoyt and one sided Gaussian distributions. Similarly, the inverse Gaussian (IG) distribution is a convenient model which was recently shown to characterize shadowing more efficiently than the widely used gamma distribution. To this effect, the proposed η-μ/IG model provides an overall efficient characterization of multipath and shadowing effects which typically occur simultaneously. The offered modelling accuracy is achieved thanks to the remarkable flexibility of its parameters. This is also verified by the fact that the proposed model is capable of providing good fittings to experimental data that correspond to realistic wireless communication scenarios while they include as special cases the widely known Nakagami-m/IG, Rayleigh/IG and Hoyt/IG composite fading models. Novel analytic expressions are derived for the envelope and power probability density function (pdf) of the η-μ/IG model. The derived expressions can be utilized in various studies in radio communications, free space optical communications and ultrasound imaging, among others. Indicatively, an analytic expression is derived for the outage probability (OP) of η-μ/IG fading channels.