The energetic contribution of attractive hydration forces arising from water ordering is an interesting but often neglected aspect of macromolecular interactions. Ordering effects of water can bring about cooperativity in many intermolecular transactions, in both the short and long range. Given its high charge density, this is of particular importance for DNA. For instance, in nanotechnology, highly charged dendrimers are used for DNA compaction and transfection. Hypothesizing that water ordering and hydration forces should be maximal for DNA complexes that show charge complementarity (positive-negative), we present here an analysis of water ordering from molecular dynamics simulations and free energy calculations of the interaction between DNA and a nanoparticle with a high positive charge density. Our results indicate not only that complexation of the dendrimer with DNA affects the local water structure but also that ordered water molecules facilitate long-range interactions between the molecules. This contributes significantly to the free energy of binding of dendrirners to DNA and extends the interaction well beyond the electrostatic range of the DNA. Such water effects are of potentially substantial importance in cases when molecules appear to recognize each other across sizable distances, or for which kinetic rates are too fast to be due to pure diffusion. Our results are in good agreement with experiments on the role of solvent in DNA condensation by multivalent cations and exemplify a microscopic realization of mean-field phenomenological theories for hydration forces between mesoscopic surfaces.