Decays of the Ξ_{b}^{-} and Ω_{b}^{-} baryons to the charmless final states ph^{-}h^{'-}, where h^{(')} denotes a kaon or pion, are searched for with the LHCb detector. The analysis is based on a sample of proton-proton collision data collected at center-of-mass energies sqrt[s]=7 and 8 TeV, corresponding to an integrated luminosity of 3 fb^{-1}. The decay Ξ_{b}^{-}→pK^{-}K^{-} is observed with a significance of 8.7 standard deviations, and evidence at the level of 3.4 standard deviations is found for the Ξ_{b}^{-}→pK^{-}π^{-} decay. Results are reported, relative to the B^{-}→K^{+}K^{-}K^{-} normalization channel, for the products of branching fractions and b-hadron production fractions. The branching fractions of Ξ_{b}^{-}→pK^{-}π^{-} and Ξ_{b}^{-}→pπ^{-}π^{-} relative to Ξ_{b}^{-}→pK^{-}K^{-} decays are also measured.