Aging is a ubiquitous phenomenon in glasses. In the case of phase-change materials, it leads to a drift in the electrical resistance, which hinders the development of ultrahigh density storage devices. Here we elucidate the aging process in amorphous GeTe, a prototypical phase-change material, by advanced numerical simulations, photothermal deflection spectroscopy and impedance spectroscopy experiments. We show that aging is accompanied by a progressive change of the local chemical order towards the crystalline one. Yet, the glass evolves towards a covalent amorphous network with increasing Peierls distortion, whose structural and electronic properties drift away from those of the resonantly bonded crystal. This behaviour sets phase-change materials apart from conventional glass-forming systems, which display the same local structure and bonding in both phases.