The observation of Higgs boson production in association with a top quark pair (t (t) over barH), based on the analysis of proton-proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the Large Hadron Collider, is presented. Using data corresponding to integrated luminosities of up to 79.8 fb(-1), and considering Higgs boson decays into b (b) over bar, WW*, tau(+)tau(-), gamma gamma, and ZZ*, the observed significance is 5.8 standard deviations, compared to an expectation of 4.9 standard deviations. Combined with the t (t) over barH searches using a dataset corresponding to integrated luminosities of 4.5 fb(-1) at 7 TeV and 20.3 fb(-1) at 8 TeV, the observed (expected) significance is 6.3 (5.1) standard deviations. Assuming Standard Model branching fractions, the total t (t) over barH production cross section at 13 TeV is measured to be 670 +/- 90(stat.)(-100)(+110)(syst.) fb, in agreement with the Standard Model prediction. (c) 2018 The Author(s). Published by Elsevier B.V.