Aims.We constrain the evolution of the galaxy mass and luminosity functions from the analysis of (public) multi-wavelength data in the Chandra Deep Field South (CDFS) area, obtained from GOODS and other projects, including very deep high-resolution imaging by HST/ACS. Methods.Our reference catalogue of faint high-redshift galaxies, which we have thoroughly tested for completeness and reliability, comes from a deep (S3.6≥ 1 μJy) image by IRAC on the Spitzer Observatory. These imaging data in the field are complemented by extensive optical spectroscopy by the ESO VLT/FORS2 and VIMOS spectrographs, while deep K-band VLT/ISAAC imaging is also used to derive further complementary statistical constraints and to assist the source identification and Spectral Energy Distribution (SED) analysis. We selected a highly reliable IRAC 3.6 μm sub-sample of 1478 galaxies with S3.6≥ 10 μJy, 47% of which have spectroscopic redshift, while for the remaining objects we used both COMBO-17 data (Wolf et al. 2004, A&A, 421, 913) and the code Hyperz (Bolzonella et al. 2000, A&A, 363, 476) to estimate the photometric redshift. This very extensive dataset was exploited to assess evolutionary effects in the galaxy luminosity and stellar mass functions, while luminosity/density evolution is further constrained with the number counts and redshift distributions. The deep ACS imaging allows us to differentiate between these evolutionary paths by morphological type, which our simulations show to be reliable at least up to z˜ 1.5 for the two main early- (E/S0) and late-type (Sp/Irr) classes. Results.These data, as well as our direct estimate of the stellar mass function above M_ast h^2=1010 M_sun for the spheroidal subclass, consistently show a progressive dearth of such objects starting at z˜ 0.7, paralleled by an increase in luminosity. A similar trend, with a more modest decrease in the mass function, is also shared by spiral galaxies, while the irregulars/mergers show an increased incidence at higher z. Remarkably, this decrease in the comoving density with redshift of the total population appears to depend on galaxy mass, being stronger for moderate-mass galaxies, but almost absent until z=1.4 for high-mass galaxies, thus confirming previous evidence of a “downsizing” effect in galaxy formation. Conclusions.Our favoured interpretation of the evolutionary trends for the two galaxy categories is that of a progressive morphological transformation (due to gas exhaustion and, likely, merging) from the star-forming to the passively evolving phase, starting at z≥ 2 and holding on down to z˜ 0.7. The rate of this process appears to depend on galaxy mass, being already largely settled by z˜ 1 for the most massive systems.