The Ξ_{b}^{0(-)}→Ξ_{c}(3055)^{+(0)}(→D^{+(0)}Λ)π^{-} decay chains are observed, and the spin-parity of Ξ_{c}(3055)^{+(0)} baryons is determined for the first time. The measurement is performed using proton-proton collision data at a center-of-mass energy of sqrt[s]=13 TeV, corresponding to an integrated luminosity of 5.4 fb^{-1}, recorded by the LHCb experiment between 2016 and 2018. The spin-parity of the Ξ_{c}(3055)^{+(0)} baryons is determined to be 3/2^{+} with a significance of more than 6.5σ (3.5σ) compared to all other tested hypotheses. The up-down asymmetries of the Ξ_{b}^{0(-)}→Ξ_{c}(3055)^{+(0)}π^{-} transitions are measured to be -0.92±0.10±0.05 (-0.92±0.16±0.22), consistent with maximal parity violation, where the first uncertainty is statistical and the second is systematic. These results support the hypothesis that the Ξ_{c}(3055)^{+(0)} baryons correspond to the first D-wave λ-mode excitation of the Ξ_{c} flavor triplet.