A measurement is presented of differential cross sections for Higgs boson (H) production in pp collisions at root s = 8 TeV. The analysis exploits the H -> gamma gamma decay in data corresponding to an integrated luminosity of 19.7 fb(-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 vertical bar eta vertical bar < 2.5, and with the photon of largest and next-to-largest transverse momentum (p(T)(gamma)) divided by the diphoton mass m(gamma gamma) satisfying the respective conditions of p(T)(gamma)/m(gamma gamma) > 1/3 and > 1/4, the total fiducial cross section is 32 +/- 10 fb.