We report the observation of the rare charm decay D^{0}→K^{-}π^{+}e^{+}e^{-}, based on 468 fb^{-1} of e^{+}e^{-} annihilation data collected at or close to the center-of-mass energy of the ϒ(4S) resonance with the BABAR detector at the SLAC National Accelerator Laboratory. We find the branching fraction in the invariant mass range 0.675<m(e^{+}e^{-})<0.875 GeV/c^{2} of the electron-positron pair to be B(D^{0}→K^{-}π^{+}e^{+}e^{-})=(4.0±0.5±0.2±0.1)×10^{-6}, where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty in the branching fraction of the decay D^{0}→K^{-}π^{+}π^{+}π^{-} used as a normalization mode. The significance of the observation corresponds to 9.7 standard deviations including systematic uncertainties. This result is consistent with the recently reported D^{0}→K^{-}π^{+}μ^{+}μ^{-} branching fraction, measured in the same invariant mass range, and with the value expected in the standard model. In a set of regions of m(e^{+}e^{-}), where long-distance effects are potentially small, we determine a 90% confidence level upper limit on the branching fraction B(D^{0}→K^{-}π^{+}e^{+}e^{-})<3.1×10^{-6}.