Several studies have tried to ascertain whether or not the increase in abundance of the early-type galaxies (E-S0as) with time is mainly due to major mergers, reaching opposite conclusions. We have tested it directly through semi-analytical modelling, by studying how the massive early-type galaxies with log(M_*/Msun)>11 at z~0 (mETGs) would have evolved backwards-in-time, under the hypothesis that each major merger gives place to an early-type galaxy. The study was carried out just considering the major mergers strictly reported by observations at each redshift, and assuming that gas-rich major mergers experience transitory phases of dust-reddened, star-forming galaxies (DSFs). The model is able to reproduce the observed evolution of the galaxy LFs at z<~1, simultaneously for different rest-frame bands (B, I, and K) and for different selection criteria on color and morphology. It also provides a framework in which apparently-contradictory results on the recent evolution of the luminosity function (LF) of massive, red galaxies can be reconciled, just considering that observational samples of red galaxies can be significantly contaminated by DSFs. The model proves that it is feasible to build up ~50-60% of the present-day mETG population at z<~1 and to reproduce the observational excess by a factor of ~4-5 of late-type galaxies at 0.8<z<1 through the coordinated action of wet, mixed, and dry major mergers, fulfilling global trends that are in general agreement with mass-downsizing. The bulk of this assembly takes place during ~1 Gyr elapsed at 0.8<z<1. The model suggests that major mergers have been the main driver for the observational migration of mass from the massive-end of the blue galaxy cloud to that of the red sequence in the last ~8 Gyr.(Abridged)
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