The evolution of BCGs is important for understanding galaxy assembly history within galaxy clusters, but observationally it is hard to define BCG progenitors beyond z~1. In this work, we develop a novel method for identifying BCG progenitors at z~2 and tracing the evolution of BCGs since that time. We conclude from simulations that the best method to construct BCG progenitor sample at z~2 is to use a hybrid environmental density and stellar mass ranking approach by which 44.5% of BCG progenitors can be retrieved. Applying this method on CANDELS UDS data, we construct our z~2 BCG progenitor sample. We furthermore select our local comparisons from SDSS with statistically likely contamination to ensure a fair comparison between high and low redshifts. Using these observational samples, we find that the size of BCGs has grown by a factor of 3.2 since z~2, and BCG progenitors are mainly late-type galaxies. BCG progenitors have more disturbed morphologies: 32% of them are undergoing mergers or will undergo mergers. In contrast, local BCGs are early-type galaxies having much smoother morphologies. We find that the stellar mass of BCGs has grown by a factor of 2.5 since z~2, and the SFR of BCG progenitors is much higher than their quiescent local descendants. We demonstrate that over z=1-2 SF and merging contribute equally to BCG mass growth. However, since SFR decreases with time, merging play a more dominant role in BCG assembly at redshifts lower than 1.