  The observation of Higgs boson production in association with a top quark
pair ($t\bar{t}H$), 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
$b\bar{b}$, $WW^*$, $\tau\tau$, $\gamma\gamma$, and $ZZ^*$, the observed
significance is 5.8 standard deviations, compared to an expectation of 4.9
standard deviations. Combined with the $t\bar{t}H$ 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 $t\bar{t}H$
production cross section at 13 TeV is measured to be 670 $\pm$ 90 (stat.)
$^{+110}_{-100}$ (syst.) fb, in agreement with the Standard Model prediction.
