Decays of B0 and Bs0 mesons to the charmless baryonic final states pp-h+h′-, where h and h′ each denote a kaon or a pion, are searched for using the LHCb detector. The analysis is based on a sample of proton-proton collision data collected at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb-1. Four-body charmless baryonic Bs0 decays are observed for the first time. The decays Bs0→pp-K+K-, Bs0→pp-K±πâ", B0→pp-K±πâ" and B0→pp-π+π-A re observed with a significance greater than 5 standard deviations; evidence at 4.1 standard deviations is found for the B0→pp-K+K-decay and an upper limit is set on the branching fraction for Bs0→pp-π+π-. Branching fractions in the kinematic region m(pp-)<2850 MeV/c2 are measured relative to the B0→J/ψ(→pp-)K∗(892)0 channel.