This work is devoted to the formulation and derivation of the $κ-μ$/gamma distribution which corresponds to A physical fading model. This distribution is composite and is based on the well known $κ-μ$ generalized multipath model and the gamma shadowing model. A special case of the derived model constitutes the $κ-μ$ Extreme/gamma model which accounts for severe multipath and shadowing effects. These models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects. This is achieved thanks to the remarkable flexibility of their named parameters which render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is additionally justified by the fact that they include as special cases the widely known composite fading models such as Rice/gamma, Nakagami-m/gamma and Rayleigh/gamma. Novel analytic expressions are derived for the envelope and power probability density function of these distributions which are expressed in a relatively simple algebraic form which is convenient to handle both analytically and numerically. As a result, they can be meaningfully utilized in the derivation of numerous vital measures in investigations related to the analytic performance evaluation of digital communications over composite multipath/shadowing fading channels.