The terahertz (THz) response of solvated electrons in liquid water is studied in nonlinear ultrafast pump-probe experiments. Free electrons with concentrations from c_{e}=4 to 140×10^{-6} moles/liter are generated by high-field THz or near-infrared multiphoton excitation. The time-resolved change of the dielectric function as mapped by broadband THz pulses exhibits pronounced oscillations persisting up to 30 ps. Their frequency increases with electron concentration from 0.2 to 1.5 THz. The oscillatory response is assigned to impulsively excited coherent polarons involving coupled electron and water shell motions with a frequency set by the local electric field.