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 } \leq \rho _ { t } \leq 0.065 fm ^ { -3 } and 0.01 MeV/fm ^ { 3 } \leq P _ { t } \leq 0.26 MeV/fm ^ { 3 } , respectively . Implications of these constraints on the Vela pulsar are discussed .