The interplay between electron correlation and nuclear quantum effects makes our understanding of elemental hydrogen a formidable challenge. Here, we present the phase diagram of hydrogen and deuterium at low temperatures and high-pressure (P > 300 GPa) by accounting for highly accurate electronic and nuclear enthalpies. We evaluated internal electronic energies by diffusion quantum Monte Carlo, while nuclear quantum motion and anharmonicity have been included by the stochastic self-consistent harmonic approximation. Our results show that the long-sought atomic metallic hydrogen, predicted to host room-temperature superconductivity, forms at 577±10 GPa (640±14 GPa in deuterium). Indeed, anharmonicity pushes the stability of this phase towards pressures much larger than previous theoretical estimates or attained experimental values. Before atomization, molecular hydrogen transforms from a metallic phase III to another metallic structure that is still molecular (phase VI) at 422±40 GPa (442±30 GPa in deuterium). We predict clear-cut signatures in optical spectroscopy and DC conductivity that can be used experimentally to distinguish between the two structural transitions. According to our findings, the experimental evidence of metallic hydrogen has so far been limited to molecular phases. The data uploaded here contains the structural information of the simulated phases of hydrogen and their quantum centroid position as a function of pressure and isotope.