In the context of the minimal supersymmetric seesaw model, the CP-violating neutrino Yukawa couplings might induce an electron electric dipole moment (EDM). The same interactions may also be responsible for the generation of the observed baryon asymmetry of the universe via leptogenesis. In the framework of mSUGRA, we identify in a model-independent way those patterns within the seesaw models which predict, barring unnatural cancelations, an electron EDM at a level probed by planned laboratory experiments and show that negative searches on τ→eγ decay may provide the strongest upper bound on the electron EDM. We also conclude that a possible future detection of the electron EDM is incompatible with thermal leptogenesis, even when flavor effects are accounted for.