Abstract : Two structures are observed close to the kinematic threshold in the Ξ0bπ− mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb−1 recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content bds are expected in this mass region: the spin-parity JP=12+ and JP=32+ states, denoted Ξ′−b and Ξ∗−b. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to bem(Ξ′−b)−m(Ξ0b)−m(π−)=3.653±0.018±0.006 MeV/c2,m(Ξ∗−b)−m(Ξ0b)−m(π−)=23.96±0.12±0.06 MeV/c2,Γ(Ξ∗−b)=1.65±0.31±0.10 MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of Γ(Ξ′−b)<0.08 MeV at 95% confidence level. Relative production rates of these states are also reported.