A measurement is presented of differential cross sections for Higgs boson (H) production in pp collisions at √s =8 TeV. The analysis exploits the H→γγ decay in data corresponding to an integrated luminosity of 19.7fb -1 collected by the CMS experiment at the LHC. The cross section is measured as a function of the kinematic properties of the diphoton system and of the associated jets. Results corrected for detector effects are compared with predictions at next-to-leading order and next-to-next-to-leading order in perturbative quantum chromodynamics, as well as with predictions beyond the standard model. For isolated photons with pseudorapidities |η|<2.5, and with the photon of largest and next-to-largest transverse momentum (p γ T) divided by the diphoton mass m γγ satisfying the respective conditions of p γ T /m γγ >1/3 and >1/4, the total fiducial cross section is 32±10 \,fb.