A search for the Standard Model Higgs boson in proton-proton collisions with the ATLAS detector at the LHC is presented. The datasets used correspond to integrated luminosities of approximately 4.8 fb(-1) collected at, root s = 7 TeV in 2011 and 5.8 fb(-1) at root s = 8 TeV in 2012. Individual searches in the channels H -> ZZ(()*()) -> 4l, H -> gamma gamma and H -> WW (()*()) -> ev μv in the 8 TeV data are combined with previously published results of searches for H -> ZZ(()*()), WW(*()), b (b) over bar and tau(+)tau(-) in the 7 TeV data and results from improved analyses of the H -> ZZ(()*()) -> 4l and H -> gamma gamma channels in the 7 TeV data. Clear evidence for the production of a neutral boson with a measured mass of 126.0 +/- 0.4 (stat) +/- 0.4 (sys) GeV is presented. This observation, which has a significance of 5.9 standard deviations, corresponding to a background fluctuation probability of 1.7 x 10(-9), is compatible with the production and decay of the Standard Model Higgs boson.