The first observation of the decay of a B^{0} meson to a purely baryonic final state, B^{0}→pp[over ¯], is reported. The proton-proton collision data sample used was collected with the LHCb experiment at center-of-mass energies of 7 and 8 TeV and corresponds to an integrated luminosity of 3.0 fb^{-1}. The branching fraction is determined to be B(B^{0}→pp[over ¯])=(1.25±0.27±0.18)×10^{-8}, where the first uncertainty is statistical and the second systematic. The decay mode B^{0}→pp[over ¯] is the rarest decay of the B^{0} meson observed to date. The decay B_{s}^{0}→pp[over ¯] is also investigated. No signal is seen and the upper limit B(B_{s}^{0}→pp[over ¯])<1.5×10^{-8} at 90% confidence level is set on the branching fraction.