The first observation and study of two new baryonic structures in the final state Ξ_{b}^{0}π^{+}π^{-} and the confirmation of the Ξ_{b}(6100)^{-} state in the Ξ_{b}^{-}π^{+}π^{-} decay mode are reported using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb^{-1}. In addition, the properties of the known Ξ_{b}^{*0}, Ξ_{b}^{'-} and Ξ_{b}^{*-} resonances are measured with improved precision. The new decay mode of the Ξ_{b}^{0} baryon to the Ξ_{c}^{+} π^{-} π^{+} π^{-} final state is observed and exploited for the first time in these measurements.