Using data recorded in 2011 with the ATLAS detector at the Large Hadron Collider, a search for evidence of extra spatial dimensions has been performed through an analysis of the diphoton final state. The analysis uses data corresponding to an integrated luminosity of 2.12 fb(-1) of root s = 7 TeV proton-proton collisions. The diphoton invariant mass (m(gamma gamma)) spectrum is observed to be in good agreement with the expected Standard Model background. In the large extra dimension scenario of Arkani-Hamed, Dimopoulos and Dvali, the results provide 95% CL lower limits on the fundamental Planck scale between 2.27 and 3.53 TeV, depending on the number of extra dimensions and the theoretical formalism used. The results also set 95% CL lower limits on the lightest Randall-Sundrum graviton mass of between 0.79 and 1.85 TeV, for values of the dimensionless coupling k/(M) over bar (Pl) varying from 0.01 to 0.1. Combining with previously published ATLAS results from the dielectron and dimuon final states, the 95% CL lower limit on the Randall-Sundrum graviton mass for k/(M) over bar (Pl) = 0.01 (0.1) is 0.80 (1.95) TeV.