K-band galaxy number counts (GNCs) exhibit a slope change at K ˜ 17.5 mag not present in optical bands. To unveil the nature of this feature, we have derived the contribution of different galaxy types to the total K-band GNCs at 0.3 < z < 1.5 by redshift bins and compared the results with expectations from several galaxy evolutionary models. We show that the slope change is caused by a sudden swap of the galaxy population that numerically dominates the total GNCs (from quiescent E-S0's at K < 17.5 mag to blue star-forming discs at fainter magnitudes), and that it is associated with a flattening of the contribution of the E-S0's at 0.6 < z < 1 to the total GNCs. We confirm previous studies showing that models in which the bulk of massive E-S0's have evolved passively since z > 2 cannot predict the slope change, whereas those imposing a relatively late assembly on them (z < 1.5) can reproduce it. The K-band GNCs by redshift bins and morphological types point to a progressively definitive build-up of ˜50 per cent of this galaxy population at 0.8 < z < 1.5, which can be explained only through the major mergers reported by observations. We conclude that the slope change in total K-band GNCs is a vestige of the definitive assembly of a substantial fraction of present-day massive E-S0's at 0.8 < z < 1.5.