Binding of excess electrons to nanosize water droplets, with a focus on the hitherto largely unexplored properties of doubly-charged clusters, were investigated experimentally using mass spectrometry and theoretically with large-scale first-principles simulations based on spin-density-functional theory, with all the valence electrons (that is, 8e per water molecule) and excess electrons treated quantum mechanically. Singly-charged clusters (H(2)O)(n)(-1) were detected for n = 6 - 250, and our calculated vertical detachment energies agree with previously measured values in the entire range 15 <= n <= 105, giving a consistent interpretation in terms of internal, surface and diffuse states of the excess electron. Doubly-charged clusters were measured in the range of 83 <= n <= 123, with (H(2)O)(n)(-2) clusters found for 83 <= n < 105, and mass-shifted peaks corresponding to (H(2)O)(n-2) (OH(-))(2) detected for n >= 105. The simulations revealed surface and internal dielectron, e(2)(-), localization modes and elucidated the mechanism of the reaction (H(2)O)(n)(-2) -> (H(2)O)(n-2) (OH(-))(2) + H(2) (for n >= 105), which was found to occur via concerted approach of a pair of protons belonging to two water molecules located in the first shell of the dielectron internal hydration cavity, culminating in formation of a hydrogen molecule 2H(+) + e(2)(-) -> H(2). Instability of the dielectron internal localization impedes the reaction for smaller (n < 105) doubly-charged clusters.