This paper presents a proof of the uniqueness theorem for the initial boundary value problem governing advective-diffusive transport of a chemical in a fluid-saturated non-deformable isotropic, homogeneous porous medium. The advective Darcy flow in the porous medium results from the gradient of a hydraulic potential, which is derived from a well-posed problem in potential theory. The paper discusses the relevant set of consistent boundary conditions applicable to the potential inducing the advective flow and to the concentration field, which ensures uniqueness of the solution.