Al-Zn-Mg alloys stand among the strongest Al alloys due to the interaction of Guinier-Preston (GP) zones and η′ precipitates with dislocations. Understanding the process of precipitate nucleation is critical to design age-hardenable Al-Zn-Mg alloys with improved mechanical properties. In this investigation, the structure and formation path of GP zones, η′ and η precipitates was studied by means of first principles calculations and statistical mechanics. The structures of potential GP configurations on the FCC convex hull were revealed as well as the presence in the convex hull of FCC MgZn2 clusters. They were found to be precursors of η′ precipitates because of the formation of stacking faults. The η′-to-η transformation was governed by the advance of the η′ interface towards the FCC MgZn2 cluster, so the equilibrium η precipitate is the result of the growth and coarsening of η′. Finally, the critical nucleation temperature for η′ precipitates was determined from the thermodynamic driving force of the transformation. These results rationalize the experimental data available in the literature and offer insights to enhance the strength of Al-Zn-Mg alloys.