The observation of Higgs boson production in association with a top quark pair (tt¯H), 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, WW∗, τ+τ−, γγ, and ZZ∗, the observed significance is 5.8 standard deviations, compared to an expectation of 4.9 standard deviations. Combined with the t¯tH searches using a dataset corresponding to integrated luminosities of 4.5 fb−1at 7TeVand 20.3 fb−1at 8TeV,the observed (expected) significance is 6.3 (5.1) standard deviations. Assuming Standard Model branching fractions, the total t¯tH production cross section at 13 TeV is measured to be 670 ± 90 (stat.)+110−100(syst.) fb, in agreement with the Standard Model prediction.