A two-component model of the solar photosphere is obtained from the inversion of the intensity profiles of 22 Fe I spectral lines for which very accurate atomic data (oscillator strengths, central wavelengths, and collisional broadening parameters) exist. The model is meant to describe the effects of convective motions in the solar photosphere. It has been subject to various tests to confront its predictions with observations of the solar spectrum. The model is able to reproduce the observed line shifts and equivalent widths of about 800 spectral lines of iron and other species. It is also capable of matching the observed center-to-limb variation of the continuum intensity with unprecedented accuracy. This allows us to determine line-transition parameters from the fitting of the solar spectrum. Exploratory calculations demonstrate that the model can be used to derive transition probabilities and central wavelengths of Fe I and Fe II lines, as well as other elements, within the uncertainties of the best laboratory measurements.