This article documents the muon reconstruction and identification efficiency obtained by the ATLAS experiment for 139 fb-1 of pp collision data at <mml:msqrt>s</mml:msqrt>=13 TeV collected between 2015 and 2018 during Run 2 of the LHC. The increased instantaneous luminosity delivered by the LHC over this period required a reoptimisation of the criteria for the identification of prompt muons. Improved and newly developed algorithms were deployed to preserve high muon identification efficiency with a low misidentification rate and good momentum resolution. The availability of large samples of Z -> mu mu and J/psi -> mu mu decays, and the minimisation of systematic uncertainties, allows the efficiencies of criteria for muon identification, primary vertex association, and isolation to be measured with an accuracy at the per-mille level in the bulk of the phase space, and up to the percent level in complex kinematic configurations. Excellent performance is achieved over a range of transverse momenta from 3 GeV to several hundred GeV, and across the full muon detector acceptance of |eta|<2.7.