The algorithms used by the ATLAS Collaboration to reconstruct and identify prompt photons are described. Measurements of the photon identification efficiencies are reported, using 4.9 fb[Formula: see text] of pp collision data collected at the LHC at [Formula: see text] [Formula: see text] and 20.3 fb[Formula: see text] at [Formula: see text] [Formula: see text]. The efficiencies are measured separately for converted and unconverted photons, in four different pseudorapidity regions, for transverse momenta between 10 [Formula: see text] and 1.5 [Formula: see text]. The results from the combination of three data-driven techniques are compared to the predictions from a simulation of the detector response, after correcting the electromagnetic shower momenta in the simulation for the average differences observed with respect to data. Data-to-simulation efficiency ratios used as correction factors in physics measurements are determined to account for the small residual efficiency differences. These factors are measured with uncertainties between 0.5% and 10% in 7 [Formula: see text] data and between 0.5% and 5.6% in 8 [Formula: see text] data, depending on the photon transverse momentum and pseudorapidity.