Solvent-based separation systems have a substantial potential for improvement when the solvent and the process conditions are optimized simultaneously. The fully integrated design problem, however, leads to an optimization problem of prohibitive size and complexity owing to the many discrete degrees of freedom in selecting a solvent and the nonlinear nature of the process models. We here implement and extend the method of continuous molecular targeting computer-aided molecular design (CoMT-CAMD) for the solvent and process optimization of a precombustion CO2-capture system with physical absorption. CoMT-CAMD is a deterministic procedure that does not require a preselection of solvent molecules. The process topology considered in our study includes all major process operations of an existing CO2-capture system: multistage absorption, desorption (two flash desorption stages with gas recycle) and CO2 compression. We measure the process performance with a single economic objective function. The objective function captures the process trade-offs and evaluates the potential process-solvent on a common basis. The solvent is represented as the pure component parameters of the perturbed-chain statistical associating fluid theory (PC-SAFT). The optimization problem is formulated with the pure component parameters of the solvent (PC-SAFT parameters) and with the process variables as degrees of freedom. Necessary auxiliary properties of the optimized solvent such as the ideal gas heat capacity and the molar mass are predicted with quantitative structure property relationship models, based on the pure component PC-SAFT parameters. As a result, one gets a unified thermodynamic framework for fluid properties based on the PC-SAFT model. With CoMT-CAMD we obtain a list of the best performing physical solvents for the considered CO2-capture application. The resulting list of best performing solvents contains state-of-the-art solvents and new green solvent molecules.