Fracture‐matrix interactions can significantly affect solute transport in fractured porous media and rocks, even when fractures are major (or sole) conduits of flow. We develop a semi‐analytical solution for transport of conservative solutes in a single fracture. Our solution accounts for two‐dimensional dispersion in the fracture, two‐dimensional diffusion in the ambient matrix, and fully coupled fracture‐matrix exchange, without resorting to simplifying assumptions regarding any of these transport mechanisms. It also enables one to deal with arbitrary initial and boundary conditions, as well as with distributed and point sources. We investigate the impact of transverse dispersion in a fracture and longitudinal diffusion in the ambient matrix on the fracture‐matrix exchange, both of which are neglected in standard models of transport in fractured media.