We present an evaluation of the complete gauge-invariant set of the two-loop self-energy diagrams carried out to all orders in the parameter Zα. The calculation is performed for the ground state of H-like ions with Z ≥ 40. As a result, we significantly improve the accuracy of theoretical values for the ground-state Lamb shift in high-Z H-like ions. We provide a compilation of various contributions to the ground-state energy of H-like ions and estimate uncertainties of the corresponding theoretical predictions.