Two structures are observed close to the kinematic threshold in the Ξb0π- mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0fb-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=(1/2)+ and JP=(3/2)+ states, denoted Ξb′- and Ξb∗-. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be m(Ξb′-)-m(Ξb0)-m(π-)=3.653±0.018±0.006MeV/c2, m(Ξb∗-)-m(Ξb0)-m(π-)=23.96±0.12±0.06MeV/c2, Γ(Ξb∗-)=1.65±0.31±0.10MeV, 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(Ξb′-)<0.08MeV at 95% confidence level. Relative production rates of these states are also reported.