We provide a consistent description of the electronic levels associated with localized and delocalized excess electrons in liquid water by combining hybrid-functional molecular dynamics simulations with a grand canonical formulation of solutes in aqueous solution. The excess electron localizes in a cavity with an average radius of 1.8 angstrom and a majority coordination of five water molecules. The vertical binding energy, the optical s p transitions, and the adiabatic redox level are found to agree closely with their experimental counterparts. The energy level associated with electron delocalization V-0 is inferred to lie at -0.97 eV with respect to the vacuum level.