Advanced reactive transport models of fluid flow and solute transport in subsurface porous media are instrumental for the assessment of contaminant environmental fate and for the design of in situ remediation interventions. However, the increasing complexity of process‐based reactive transport simulators often leads to long runtimes, which poses severe restrictions for tasks that require numerous model evaluations. To overcome this limitation, we demonstrate how machine learning surrogate models, trained on the outputs of a limited number of process‐based reactive transport simulations, can predict the evolution of complex subsurface systems. We focus on electrokinetic enhanced bioremediation of chlorinated solvents in low‐permeability porous media, which is an in situ remediation technology entailing a suite of complex and coupled physical, chemical, and biological processes. A process‐based, multicomponent reactive transport model, capable of describing the key mechanisms of electrokinetic flow and transport, is setup in a two‐dimensional domain. The model accounts for electromigration and electroosmosis, the electrostatic interactions between charged species, the chemistry of the pore water solution, the microbially mediated degradation of the organic compounds, and the dynamics of different degraders. We develop a response surface surrogate framework using an artificial neural network as approximation function and we show that the surrogate model has the capability and the flexibility to capture the complex dynamics of electrokinetic remediation in subsurface porous media and allows computationally efficient model exploration, sensitivity analysis, and uncertainty quantification.