We report an observation of the process J/ψ→γX(1835)→γK_{S}^{0}K_{S}^{0}η at low K_{S}^{0}K_{S}^{0} mass with a statistical significance larger than 12.9σ using a data sample of 1.31×10^{9} J/ψ events collected with the BESIII detector. In this region of phase space the K_{S}^{0}K_{S}^{0} system is dominantly produced through the f_{0}(980). By performing a partial wave analysis, we determine the spin parity of the X(1835) to be J^{PC}=0^{-+}. The mass and width of the observed X(1835) are 1844±9(stat)_{-25}^{+16}(syst) MeV/c^{2} and 192_{-17}^{+20}(stat)_{-43}^{+62}(syst) MeV, respectively, which are consistent with the results obtained by BESIII in the channel J/ψ→γπ^{+}π^{-}η^{'}.