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 bb¯ , 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 tt¯H 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 tt¯H production cross section at 13 TeV is measured to be 670 ± 90 (stat.) −100+110 (syst.) fb, in agreement with the Standard Model prediction.