ABSTRACTWe investigate the formation of brightest cluster galaxies (BCGs) in the TNG300 cosmological simulation of the IllustrisTNG project. Our cluster sample consists of 700 haloes with $M_{\rm 200}\ge 5 \times 10^{13} \, {\rm M}_{⊙ }$ at z = 0, along with their progenitors at earlier epochs. This includes 280 systems with $M_{\rm 200}\ge 10^{14} \, {\rm M}_{⊙ }$ at z = 0, as well as three haloes with $M_{\rm 200}\ge 10^{15} \, {\rm M}_{⊙ }$. We find that the stellar masses and star formation rates of our simulated BCGs are in good agreement with observations at z ≲ 0.4, and that they have experienced, on average, ∼2 (∼3) major mergers since z = 1 (z = 2). Separating the BCG from the intracluster light (ICL) by means of a fixed 30 kpc aperture, we find that the fraction of stellar mass contributed by ex situ (i.e. accreted) stars at z = 0 is approximately 70, 80, and 90 per cent for the BCG, BCG + ICL, and ICL, respectively. Tracking our simulated BCGs back in time using the merger trees, we find that they became dominated by ex situ stars at z ∼1–2, and that half of the stars that are part of the BCG at z = 0 formed early (z ∼ 3) in other galaxies, but ‘assembled’ onto the BCG until later times (z ≈ 0.8 for the whole sample, z ≈ 0.5 for BCGs in $M_{\rm 200}\ge 5 \times 10^{14} \, {\rm M}_{⊙ }$ haloes). Finally, we show that the stellar mass profiles of BCGs are often dominated by ex situ stars at all radii, with stars from major mergers being found closer to the centre, while stars that were tidally stripped from other galaxies dominate the outer regions.