We present deep photometry in the B, V and I filters from CTIO/MOSAIC for about 270 000 stars in the Fornax dwarf spheroidal galaxy, out to a radius of rell ≈ 0.8 degrees. By combining the accurately calibrated photometry with the spectroscopic metallicity distributions of individual red giant branch stars we obtain the detailed star formation and chemical evolution history of Fornax. Fornax is dominated by intermediate age (1-10 Gyr) stellar populations, but also includes ancient (10-14 Gyr), and young (≤1 Gyr) stars. We show that Fornax displays a radial age gradient, with younger, more metal-rich populations dominating the central region. This confirms results from previous works. Within an elliptical radius of 0.8 degrees, or 1.9 kpc from the centre, a total mass in stars of 4.3 × 107 M⊙ was formed, from the earliest times until 250 Myr ago. Using the detailed star formation history, age estimates are determined for individual stars on the upper RGB, for which spectroscopic abundances are available, giving an age-metallicity relation of the Fornax dSph from individual stars. This shows that the average metallicity of Fornax went up rapidly from [Fe/H] ≤ -2.5 dex to [Fe/H] = -1.5 dex between 8-12 Gyr ago, after which a more gradual enrichment resulted in a narrow, well-defined sequence which reaches [Fe/H] ≈ -0.8 dex, ≈3 Gyr ago. These ages also allow us to measure the build-up of chemical elements as a function of time, and thus determine detailed timescales for the evolution of individual chemical elements. A rapid decrease in [Mg/Fe] is seen for the stars with [Fe/H] ≥ -1.5 dex, with a clear trend in age. Table 1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/544/A73