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 topologically similar normalization decays B^{0}→J/ψ(→pp[over ¯])K^{*0}(→K^{+}π^{-}) and B_{s}^{0}→J/ψ(→pp[over ¯])ϕ(→K^{+}K^{-}). The branching fractions are measured to be B(B^{0}→pp[over ¯]pp[over ¯])=(2.2±0.4±0.1±0.1)×10^{-8} and B(B_{s}^{0}→pp[over ¯]pp[over ¯])=(2.3±1.0±0.2±0.1)×10^{-8}. In these measurements, the first uncertainty is statistical, the second is systematic, and the third one is due to the external branching fraction of the normalization channel.