ABSTRACT We constrain the evolution of the brightest cluster galaxy plus intracluster light (BCG + ICL) using an ensemble of 42 galaxy groups and clusters that span redshifts of z = 0.05−1.75 and masses of M500,c= 2 × 1013−1015 M⊙. Specifically, we measure the relationship between the BCG + ICL stellar mass M⋆ and M500,c at projected radii 10 < r < 100 kpc for three different epochs. At intermediate redshift ($\bar{z}=0.40$), where we have the best data, we find M⋆ ∝ M500,c0.48 ± 0.06. Fixing the exponent of this power law for all redshifts, we constrain the normalization of this relation to be 2.08 ± 0.21 times higher at $\bar{z}=0.40$ than at high redshift ($\bar{z}=1.55$). We find no change in the relation from intermediate to low redshift ($\bar{z}=0.10$). In other words, for fixed M500,c, M⋆ at 10 < r < 100 kpc increases from $\bar{z}=1.55$ to $\bar{z}=0.40$ and not significantly thereafter. Theoretical models predict that the physical mass growth of the cluster from z = 1.5 to z = 0 within r500,c is 1.4×, excluding evolution due to definition of r500,c. We find that M⋆ within the central 100 kpc increases by ∼3.8× over the same period. Thus, the growth of M⋆ in this central region is more than a factor of 2 greater than the physical mass growth of the cluster as a whole. Furthermore, the concentration of the BCG + ICL stellar mass, defined by the ratio of stellar mass within 10 kpc to the total stellar mass within 100 kpc, decreases with increasing M500,c at all z. We interpret this result as evidence for inside–out growth of the BCG + ICL over the past 10 Gyr, with stellar mass assembly occurring at larger radii at later times.