Ionization energies for the ground state of berylliumlike ions with nuclear charge numbers in the range 16≤Z≤96 are rigorously evaluated. The calculations merge the ab initio QED treatment in the first and second orders of the perturbation theory in the fine-structure constant α with the third- and higher-order electron-correlation contributions evaluated within the Breit approximation. The nuclear recoil and nuclear polarization effects are taken into account. The accuracy of the ionization energies obtained has been significantly improved in comparison with previous calculations.