Inclusive and differential measurements of the top–antitop ($ t\overline{t} $) charge asymmetry $ {A}_{\textrm{C}}^{t\overline{t}} $ and the leptonic asymmetry $ {A}_{\textrm{C}}^{\ell \overline{\ell}} $ are presented in proton–proton collisions at $ \sqrt{s} $ = 13 TeV recorded by the ATLAS experiment at the CERN Large Hadron Collider. The measurement uses the complete Run 2 dataset, corresponding to an integrated luminosity of 139 fb$^{−1}$, combines data in the single-lepton and dilepton channels, and employs reconstruction techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure is performed to correct for detector resolution and acceptance effects. The combined inclusive $ t\overline{t} $ charge asymmetry is measured to be $ {A}_{\textrm{C}}^{t\overline{t}} $ = 0.0068 ± 0.0015, which differs from zero by 4.7 standard deviations. Differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the $ t\overline{t} $ system. Both the inclusive and differential measurements are found to be compatible with the Standard Model predictions, at next-to-next-to-leading order in quantum chromodynamics perturbation theory with next-to-leading-order electroweak corrections. The measurements are interpreted in the framework of the Standard Model effective field theory, placing competitive bounds on several Wilson coefficients.