Phase change memory (PCM) cells rely on the orders of magnitude difference in resistivity between the crystalline and amorphous phases to store information. However, the temporal evolution of the resistance of the amorphous phase, commonly referred to as resistance drift, is a key challenge for the realization of multi-level PCM. In this article, we present a comprehensive description of the time-temperature dependence of the resistance variation in a PCM cell. Our model consists of a structural relaxation model and an electrical transport model. The structural relaxation model is based on the idea that the atomic configuration of the melt-quenched amorphous phase as a whole collectively relaxes towards a more favorable equilibrium state. Experimental results obtained over a wide range of temperatures and times show remarkable agreement with the proposed model.