The solubility of organic compounds in supercritical fluids can be dramatically affected by addition of a suitable cosolvent (entrainer) at small concentrations. This makes the screening of the best-suited cosolvent an important task for the supercritical technology. The present study aims to improve our fundamental understanding of solvation in supercritical CO2 with cosolvents. We address the following questions: (1) How does the solvation free energy depend on the chemical class of an organic solute and the chemical nature of co-solvents? (2) Which intermolecular interactions determine the effect of a cosolvent on the solubility of organic compounds? We performed extensive calculations of solvation free energies of monofunctional organic molecules at infinite dilution in supercritical media by the Bennett's acceptance ratio method based on fully atomistic molecular dynamics sampling. Sixteen monofunctional organic molecules were solvated in pure sc-CO2 and sc-CO2 with addition of 6 molar % of cosolvents of different chemical nature: ethanol, acetone, and n-hexane. Cosolvent-induced solubility enhancement (CISE) factors were also calculated. It was found that formation of significant number of hydrogen bonds between a solute and cosolvent molecules leads to a profound solubility enhancement. The cosolvent effect is proportional to the number of hydrogen bonds. When polar cosolvents do not form hydrogen bonds with solutes, the CISE correlates with the dipole moment of solute molecules. However, the electrostatic interactions have a small impact on the solubility enhancement compared to hydrogen bonding. Addition of a nonpolar cosolvent, n-hexane, has a very little effect on the solvation Gibbs free energy of studied small organic molecules. The observed trends were discussed in line with available experimental data.