If right-handed Majorana neutrinos are added to the standard model, then lepton-number-violating out-of-equilibrium decays of right-handed neutrinos combined with anomalous electroweak processes can generate the baryon number of the Universe. We analyze this mechanism in detail, and determine the ranges of parameters for which the correct baryon number is generated. We find that the scenario works for a wide range of parameters in the neutrino sector, including right-handed neutrino masses ranging from \ensuremath{\sim}1 TeV to \ensuremath{\sim}${10}^{19}$ GeV, depending on the assumptions made about the structure of the neutrino mass matrices.