  The $t\bar{t}$ production cross-section is measured in the lepton+jets
channel using proton$-$proton collision data at a centre-of-mass energy of
$\sqrt{s}=13$ TeV collected with the ATLAS detector at the LHC. The dataset
corresponds to an integrated luminosity of 139 fb$^{-1}$. Events with exactly
one charged lepton and four or more jets in the final state, with at least one
jet containing $b$-hadrons, are used to determine the $t\bar{t}$ production
cross-section through a profile-likelihood fit. The inclusive cross-section is
measured to be ${\sigma_{\text{inc}} = 830 \pm 0.4~ \text{(stat.)}\pm
36~\text{(syst.)}\pm 14~\text{(lumi.)}~\mathrm{pb}}$ with a relative
uncertainty of 4.6 %. The result is consistent with theoretical calculations at
next-to-next-to-leading order in perturbative QCD. The fiducial $t\bar{t}$
cross-section within the experimental acceptance is also measured.
