We report the observation of the rare charm decay D0→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 (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/c2 of the electron-positron pair to be B(D0→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 D0→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 D0→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(D0→K-π+e+e-)<3.1×10-6.