Global polarization of Ξ and Ω hyperons has been measured for the first time in Au+Au collisions at sqrt[s_{NN}]=200 GeV. The measurements of the Ξ^{-} and Ξ[over ¯]^{+} hyperon polarization have been performed by two independent methods, via analysis of the angular distribution of the daughter particles in the parity violating weak decay Ξ→Λ+π, as well as by measuring the polarization of the daughter Λ hyperon, polarized via polarization transfer from its parent. The polarization, obtained by combining the results from the two methods and averaged over Ξ^{-} and Ξ[over ¯]^{+}, is measured to be ⟨P_{Ξ}⟩=0.47±0.10(stat)±0.23(syst)% for the collision centrality 20%-80%. The ⟨P_{Ξ}⟩ is found to be slightly larger than the inclusive Λ polarization and in reasonable agreement with a multiphase transport model. The ⟨P_{Ξ}⟩ is found to follow the centrality dependence of the vorticity predicted in the model, increasing toward more peripheral collisions. The global polarization of Ω, ⟨P_{Ω}⟩=1.11±0.87(stat)±1.97(syst)% was obtained by measuring the polarization of daughter Λ in the decay Ω→Λ+K, assuming the polarization transfer factor C_{ΩΛ}=1.