The algorithms used by the ATLAS Collaboration during Run 2 of the Large Hadron Collider to identify jets containing b-hadrons are presented. The performance of the algorithms is evaluated in the simulation and the efficiency with which these algorithms identify jets containing b-hadrons is measured in collision data. The measurement uses a likelihood-based method in a sample highly enriched in tt¯ events. The topology of the t→ Wb decays is exploited to simultaneously measure both the jet flavour composition of the sample and the efficiency in a transverse momentum range from 20 to 600 GeV. The efficiency measurement is subsequently compared with that predicted by the simulation. The data used in this measurement, corresponding to a total integrated luminosity of 80.5 fb - 1, were collected in proton–proton collisions during the years 2015–2017 at a centre-of-mass energy s= 13 TeV. By simultaneously extracting both the efficiency and jet flavour composition, this measurement significantly improves the precision compared to previous results, with uncertainties ranging from 1 to 8% depending on the jet transverse momentum.