The first observation of the B(s)(0)→η'η' decay is reported. The study is based on a sample of proton-proton collisions corresponding to 3.0 fb(-1) of integrated luminosity collected with the LHCb detector. The significance of the signal is 6.4 standard deviations. The branching fraction is measured to be [3.31±0.64(stat)±0.28(syst)±0.12(norm)]×10(-5), where the third uncertainty comes from the B(±)→η'K(±) branching fraction that is used as a normalization. In addition, the charge asymmetries of B(±)→η'K(±) and B(±)→ϕK(±), which are control channels, are measured to be (-0.2±1.3)% and (+1.7±1.3)%, respectively. All results are consistent with theoretical expectations.