Searches for the rare hadronic decays B^{0}→pp[over ¯]pp[over ¯] and B_{s}^{0}→pp[over ¯]pp[over ¯] are performed using proton-proton collision data recorded by the LHCb experiment and corresponding to an integrated luminosity of 9 fb^{-1}. Significances of 9.3σ and 4.0σ, including statistical and systematic uncertainties, are obtained for the B^{0}→pp[over ¯]pp[over ¯] and B_{s}^{0}→pp[over ¯]pp[over ¯] signals, respectively. The branching fractions are measured relative to the …