[en] We show that the widely used parabolic approximation to the Equation of State (EOS) of asymmetric nuclear matter leads systematically to significantly higher core-crust transition densities and pressures. Using an EOS for neutron-rich nuclear matter constrained by the isospin diffusion data from heavy-ion reactions in the same sub-saturation density range as the neutron star crust, the density and pressure at the inner edge separating the liquid core from the solid crust of neutron stars are determined to be 0.040 fm^-3≤ρ_t≤0.065 fm^-3 and 0.01 MeV/fm³≤P_t≤0.26 MeV/fm³, respectively. Implications of these constraints on the Vela pulsar are discussed.