Clogging due to transport and accumulation of the colloids in the pore space has been recognized as one of the most significant challenges in water management research and environmental engineering. This paper proposes an inversion algorithm in time-lapse mode to track that complex process through the assessment of alteration in the transmissivity field produced by the injection of colloids. The concept is based on a joint inversion of hydraulic head and colloidal particles concentration data acquired during the injection of colloids in the porous aquifer to reconstruct the spatial variability of the transmissivity field at different times. The inversion code is deterministic and was implemented in the time-lapse scheme by adding in the objective function a temporal geostatistical constraint to control changes of the hydraulic transmissivity. This algorithm is linked to a forward problem that consists of the groundwater flow and transport equations, which were solved numerically and jointly by considering the effect of particles deposition on the decrease of hydraulic properties. As the inverse problem is deterministic and underdetermined, we have opted to use the efficient adjoint state technique to derive the sensitivity matrices. The approach has been successfully applied to a theoretical case in which the hydraulic head responses have been used alone and jointly to assess the evolution of the clogging impact on hydraulic transmissivity.