A measurement of the production cross section for two isolated photons in proton-proton collisions at a center-of-mass energy of s=8 TeV is presented. The results are based on an integrated luminosity of 20.2 fb-1 recorded by the ATLAS detector at the Large Hadron Collider. The measurement considers photons with pseudorapidities satisfying |ηγ|<1.37 or 1.56<|ηγ|<2.37 and transverse energies of respectively ET,1γ>40 GeV and ET,2γ>30 GeV for the two leading photons ordered in transverse energy produced in the interaction. The background due to hadronic jets and electrons is subtracted using data-driven techniques. The fiducial cross sections are corrected for detector effects and measured differentially as a function of six kinematic observables. The measured cross section integrated within the fiducial volume is 16.8±0.8 pb. The data are compared to fixed-order QCD calculations at next-to-leading-order and next-to-next-to-leading-order accuracy as well as next-to-leading-order computations including resummation of initial-state gluon radiation at next-to-next-to-leading logarithm or matched to a parton shower, with relative uncertainties varying from 5% to 20%.