Simplified, yet accurate, coarse-grained models are needed to explore the behavior of complex biological systems by means of Molecular Dynamics (MD) simulations, because many interesting processes occur at long time scales and large length scales that are not amenable to studies by atomistic simulations. The aqueous salt buffer provides an important contribution to the structure and function of biological molecules. While in many simplified models both water and salt are treated as a continuous medium, it is often desirable to describe mobile ions in an explicit manner. For example, the discrete nature of ions was shown to play a very important role in their interaction with highly charged biomolecules, such as DNA. In this work, we have derived an effective interaction potential for monovalent ions by systematically coarse-graining the all-atom NaCl and KCl aqueous solutions at several different ionic concentrations. Our approach is based on explicitly accounting for cross-correlations among various observables that constitute the compact basis set of the coarse-grained Hamiltonian. Compactness of the Hamiltonian ensures computational efficiency of the optimization procedure. In addition, it allows us to accurately reproduce many-body effects, in contrast with many existing algorithms. The resulting Hamiltonian produced ionic distributions that are virtually identical to those obtained in atomistic simulations with explicit water, capturing short-range hydration effects. Our coarse-grained model of monovalent electrolyte solutions allows the incorporation of ions into complex coarse-grained biomolecular simulations, where both electrostatic and short-range hydration effects must be taken into account.