The mass of the Higgs boson is measured in the H -> ZZ* -> 4l and in the H -> gamma gamma decay channels with 36.1 fb(-1) of proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The measured value in the H -> ZZ* -> 4l channel is m(H)(ZZ*) = 124.79 +/- 0.37 GeV, while the measured value in the H -> gamma gamma channel is m(H)(gamma gamma) = 124.93 +/- 0.40 GeV. Combining these results with the ATLAS measurement based on 7 and 8 TeV proton-proton collision data yields a Higgs boson mass of m(H) = 124.97 +/- 0.24 GeV.