The first measurements of differential branching fractions of inclusive semileptonic B→X_{u}ℓ^{+}ν_{ℓ} decays are performed using the full Belle data set of 711 fb^{-1} of integrated luminosity at the ϒ(4S) resonance and for ℓ=e, μ. With the availability of these measurements, new avenues for future shape-function model-independent determinations of the Cabibbo-Kobayashi-Maskawa matrix element |V_{ub}| can be pursued to gain new insights in the existing tension with respect to exclusive determinations. The differential branching fractions are reported as a function of the lepton energy, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic B→X_{c}ℓ^{+}ν_{ℓ} decays and other processes, and corrected for resolution and acceptance effects.