An aprotic lithium-air battery is a promising candidate for next-generation energy storage systems, but its practical performance is still low. The addition of water to an electrolyte can substantially increase the capacity and round-trip efficiency of batteries. However, fundamental mechanisms of the water impact are still far from being fully understood. To contribute to this issue, we studied by molecular dynamics simulations the effect of water additives on the behaviour of discharge intermediates Li+ and O2- in two frequently used solvents: dimethoxyethane (DME) and dimethyl sulfoxide (DMSO). We have estimated the structures of the solvation shells around Li+ and O2- ions, and the residence times of various electrolyte components inside the solvation shells depending on the concentration of water additives. Furthermore, we have estimated the rate and the equilibrium of the Li+ and O2- association. Our results reveal that water additives in electrolytes shift the equilibrium of the association reaction toward soluble Li+ and O2- ions in both DME and DMSO. These data argue for the view that water promotes the solution discharge mechanism, thus increasing the capacity. Moreover, we show that water accelerates the kinetics of the association reaction due to the decrease of the stability of Li+ and O2- solvation shells. This may explain the reduced discharge overpotential when water is added.