Among the phase change materials, Ge-rich GeSbTe (GST) alloys are of considerable interest as they offer a much higher thermal stability than their congruent contenders, a desirable characteristic for embedded digital memories and neuromorphic devices. Up to now, the mechanisms by which such alloys crystallize and progressively switch from one resistivity state to the other remained unclear and very controversial. Using in situ synchrotron X-ray diffraction during isothermal annealing and advanced transmission electron microscopy techniques, we solved this riddle and unveil the mechanisms leading to the overall crystallization of such alloys. During annealing at 310°C, the initially homogeneous and amorphous material undergoes a progressive phase separation leading to the formation of Ge-rich regions of different compositions. During this decomposition, first formed GeTe embryos crystallize and trigger the heterogeneous crystallization of the Ge cubic phase. As the phase separation proceeds, these embryos dissolve and the Ge phase gradually builds up through the nucleation of small grains. Only when this Ge cubic phase is largely formed, the remaining amorphous matrix may locally reach the Ge2Sb2Te5 composition at which it can crystallize as large grains. Our density functional theory calculations confirm that the quite exotic Pnma GeTe structure we have experimentally identified is more stable than the regular R3m structure at nanometric sizes.