The search for improved CO₂ capture solvents can be accelerated by deploying computer-aided molecular and process design (CAMPD) techniques to explore large molecular and process domains systematically. However, the direct solution of the integrated molecular-process design problem is very challenging as nonlinear interactions between physical properties and process performance render a large proportion of the search space infeasible. We develop a methodology that enables the direct and reliable solution of CAMPD for absorption–desorption processes, using the state-of-the-art SAFT-γ Mie group contribution approach to predict phase and chemical equilibria. We develop new feasibility tests and show them to be highly efficient at reducing the search space, integrating them in an outer-approximation algorithm. The framework is applied to design an aqueous solvent and CO₂ chemical absorption–desorption process, with 150 CAMPD instances across three case studies solved successfully. The optimal solvents are more promising than those obtained with sequential molecular design approaches.