The aim of this work is the proposition of the κ-μ/Inverse Gaussian distribution which corresponds to a physical fading model. This is a composite distribution which is based on the κ-μ multipath model and the recently proposed Inverse Gaussian shadowing model. The former is a generalised model which includes as special cases the widely known Nakagamim, Rayleigh, Rice and one sided Gaussian distributions and accounts particularly for Non-Line-of-Sight communications. The latter is a convenient model which was recently shown to characterize shadowing effect more accurately than the widely used gamma distribution. As a result, the proposed composite model provides an overall efficient characterisation of multipath and shadowing effects which typically occur simultaneously. The offered modelling accuracy is achieved thanks to the remarkable flexibility of its parameters which is verified by the fact that the model is capable of providing good fittings to measurement data from realistic communication scenarios. Novel analytic expressions are derived for the probability density function (pdf) and the moments of the κ-μ/Inverse Gaussian composite fading model which includes as special cases the Nakagami-m/Inverse Gaussian, Rayleigh/Inverse Gaussian and Rice/Inverse Gaussian composite fading distributions. The offered expressions can be readily utilized in the derivation of vital performance measures in radio and free-space-optical communications over multipath/shadowing and medium-to-strong atmospheric turbulence, respectively. In this context, a closed-form expression is derived for the Amount of Fading over κ-μ/IG fading channels.