Using the previous Belle measurement of the inclusive photon energy in B→Xsγ decays, we determine the first and second moments of this spectrum for minimum photon energies in the B meson rest frame ranging from 1.8 to 2.3 GeV. Combining these measurements with recent Belle data on the lepton energy and hadronic mass moments in B→Xcℓν decays, we perform fits to theoretical expressions derived in the 1S and kinetic mass schemes and extract the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element Vcb, the b-quark mass, and other nonperturbative parameters. In the 1S scheme analysis we find |Vcb|=(41.56±0.68(fit)±0.08(τB))×10-3 and mb1S=(4.723±0.055)GeV. In the kinetic scheme, we obtain |Vcb|=(41.58±0.69(fit)±0.08(τB)±0.58(th))×10-3 and mbkin=(4.543±0.075)GeV. © 2008 The American Physical Society.