The ATLAS detector at the Large Hadron Collider is used to search for high-mass resonances decaying to an electron-positron pair or a muon-antimuon pair. The search is sensitive to heavy neutral Z' gauge bosons, Randall-Sundrum gravitons, Z* bosons, techni-mesons, Z/gamma bosons, and bosons predicted by Torsion models. Results are presented based on an analysis of pp collisions at a center-of-mass energy of 7 TeV corresponding to an integrated luminosity of 4.9 fb(-1) in the e(+)e(-) channel and 5.0 fb(-1) in the mu(+)mu(-) channel. A Z' boson with Standard Model-like couplings is excluded at 95% confidence level for masses below 2.22 TeV. A Randall-Sundrum graviton with coupling k root M-P1 = 0.1 is excluded at 95% confidence level for masses below 2.16 Tev. Limits on the other models are also presented, including Technicolor and Minimal Z' Models.