The kinetics of chemical reactions in the liquid phase are often strongly determined by the reaction solvent. Consequently, the choice of the optimal solvent is an important task in chemical process design. Because of the vast number of potential solvents, experimental testing of all candidates is infeasible. To explore the design space of possible reaction solvents, computer-aided molecular design (CAMD) methods have been developed. However, state-of-the-art CAMD methods for reaction solvent design consider usually only a limited molecular design space and rely on simplified models fitted to experimental data to predict solvent performance. To overcome these limitations, we here propose Rx-COSMO-CAIVID as the method for the design of reaction solvents. Rx-COSMO-CAMD combines CAMD using the genetic optimization algorithm LEA3D with sound prediction of reaction kinetics based on transition-state theory and advanced quantum chemical methods. Thereby, no experimental data are required. The predictions are shown to be computationally efficient and not limited to certain structural groups. Thus, large and diverse molecular design spaces can be explored. To demonstrate the proposed Rx-COSMO-CAMD method, we successfully design solvents, enhancing the reaction kinetics of a Menschutkin reaction and a chain propagation reaction for the production of polymers and microgels. The method is shown to identify promising solvents for significant enhancement of reaction rates. Rx-COSMO-CAMD is therefore a powerful, fully predictive tool for the identification of optimal reaction solvents.