A measurement of the production cross section for two isolated photons in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ is presented. The results are based on an integrated luminosity of $20.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded by the ATLAS detector at the Large Hadron Collider. The measurement considers photons with pseudorapidities satisfying $|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|<1.37$ or $1.56<|{\ensuremath{\eta}}^{\ensuremath{\gamma}}|<2.37$ and transverse energies of respectively ${E}_{\mathrm{T},1}^{\ensuremath{\gamma}}>40\text{ }\text{ }\mathrm{GeV}$ and ${E}_{\mathrm{T},2}^{\ensuremath{\gamma}}>30\text{ }\text{ }\mathrm{GeV}$ 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 $16.8\ifmmode\pm\else\textpm\fi{}0.8\text{ }\text{ }\mathrm{pb}$. 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%.