We previously presented a thermodynamic continuum model for electrolytes. In this paper we include solvation interactions between the ions and solvent, which alter the structure of the electrochemical double layer (EDL). We combine a local solvation model with a full electrolyte model and investigate double layer structures for a wide range of electrolytes, especially including highly concentrated solutions. We find that some of the parameters of our model significantly affect the solvent concentration at the electrode surface and thereby the rate of solvent decomposition. An increased salt concentration weakens the solvation shells and eases ion desolvation at the electrode surface. The strength of the ion-solvent interaction also shifts the potential required for desolvation. Thus, our theory qualitatively predicts EDL structures for different electrolytes based on parameters like molecule size, solvent binding energy and salt concentration.