The top quark mass was measured in the channels t (t) over bar -> lepton+jets and t (t) over bar -> dilepton (lepton = e, mu) based on ATLAS data recorded in 2011. The data were taken at the LHC with a proton-proton centre-of-mass energy of root s = 7 TeV and correspond to an integrated luminosity of 4.6 fb(-1). The t (t) over bar -> lepton+jets analysis uses a three-dimensional template technique which determines the top quark mass together with a global jet energy scale factor (JSF), and a relative b-to-light-jet energy scale factor (bJSF), where the terms b-jets and light-jets refer to jets originating from b-quarks and u,d,c, s-quarks or gluons, respectively. The analysis of the t (t) over bar -> dilepton channel exploits a one-dimensional template method using the m(lb) observable, defined as the average invariant mass of the two lepton+b-jet pairs in each event. The top quark mass is measured to be 172.33 +/- 0.75(stat + JSF + bJSF) +/- 1.02(syst) GeV, and 173.79 +/- 0.54(stat) +/- 1.30(syst) GeV in the t (t) over bar -> lepton+jets and t (t) over bar -> dilepton channels, respectively. The combination of the two results yields m(top) = 172.99 +/- 0.48(stat) +/- 0.78(syst) GeV, with a total uncertainty of 0.91 GeV.