Context. Several studies have tried to ascertain whether the increase in abundance of the early-type galaxies (E-S0a's) with time is mainly due to major mergers, but have reached opposite conclusions. Aims: We have tested it directly through semi-analytical modelling, quantifying the possible contribution of the observed major mergers to the evolution of the high-mass end of the galaxy luminosity function (LF). Methods: The model analyses the backwards-in-time evolution of the massive early-type galaxies with log (M_*/M_*) > 11 at z ~ 0 (mETGs) under the hypothesis that each major merger leads to an early-type galaxy. The model considers only the major mergers strictly reported by observations at each redshift and assumes that gas-rich major mergers experience transitory phases as dust-reddened, star-forming galaxies (DSFs). Results: 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 colour and morphology. It also provides a framework in which apparently contradictory results on the recent evolution of the LF of massive red galaxies can be reconciled, just considering that observed 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 number density of mETGs at 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, providing a straightforward explanation for the observed fact that redshift z ~ 0.8 is a transition epoch in the formation of mETGs. The gas-rich progenitors of these recently assembled mETGs reproduce the observed excess by a factor of ~4-5 of late-type galaxies at 0.8 < z < 1 naturally, as compared to pure luminosity evolution (PLE) models. Conclusions: The model suggests that major mergers have been the main driver for the observed mass migration from the massive end of the blue galaxy cloud to that of the red sequence in the past ~8 Gyr.