The formation of our Milky Way can be split up qualitatively into different phases that resulted in its structurally different stellar populations: the halo and the disk components. Revealing a quantitative overall picture of our Galaxy's assembly requires a large sample of stars with very precise ages. Here we report an analysis of such a sample using subgiant stars. We find that the stellar age-metallicity distribution p({tau}, [Fe/H]) splits into two almost disjoint parts, separated at age {tau}~=8Gyr. The younger part reflects a late phase of dynamically quiescent Galactic disk formation with manifest evidence for stellar radial orbit migration4; the other part reflects the earlier phase, when the stellar halo and the old {alpha}-process-enhanced (thick) disk formed. Our results indicate that the formation of the Galaxy's old (thick) disk started approximately 13Gyr ago, only 0.8Gyr after the Big Bang, and 2Gyr earlier than the final assembly of the inner Galactic halo. Most of these stars formed around 11Gyr ago, when the Gaia-Sausage-Enceladus satellite merged with our Galaxy. Over the next 5-6Gyr, the Galaxy experienced continuous chemical element enrichment, ultimately by a factor of 10, while the star-forming gas managed to stay well mixed.