An improved measurement of the mass of the Higgs boson is derived from a combined fit to the reconstructed invariant mass spectra of the decay channels H -> gamma gamma and H -> ZZ* -> 4l. The analysis uses the pp collision data sample recorded by the ATLAS experiment at the CERN Large Hadron Collider at center-of-mass energies of 7 TeV and 8 TeV, corresponding to an integrated luminosity of 25 fb(-1). The measured value of the Higgs boson mass is m(H) = 125.36 +/- 0.37(stat) +/- 0.18 (syst) GeV. This result is based on improved energy-scale calibrations for photons, electrons, and muons as well as other analysis improvements, and supersedes the previous result from ATLAS. Upper limits on the total width of the Higgs boson are derived from fits to the invariant mass spectra of the H -> gamma gamma and H -> ZZ* -> 4l decay channels.