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This is an Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Context. The Gaia-ESO Survey (GES) is a large public spectroscopic survey that was carried out using the multi-object FLAMES spectrograph at the Very Large Telescope. The survey provides accurate radial velocities, stellar parameters, and elemental abundances for ~115 000 stars in all Milky Way components. Aims. In this paper, we describe the method adopted in the final data release to derive lithium equivalent widths (EWs) and abundances. Methods. Lithium EWs were measured using two different approaches for FGK and M-type stars, to account for the intrinsic differences in the spectra. For FGK stars, we fitted the lithium line using Gaussian components, while direct integration over a predefined interval was adopted for M-type stars. Care was taken to ensure continuity between the two regimes. Abundances were derived using a new set of homogeneous curves of growth that were derived specifically for GES, and which were measured on a synthetic spectral grid consistently with the way the EWs were measured. The derived abundances were validated by comparison with those measured by other analysis groups using different methods. Results. Lithium EWs were measured for ~40 000 stars, and abundances could be derived for ~38 000 of them. The vast majority of the measures (80%) have been obtained for stars in open cluster fields. The remaining objects are stars in globular clusters, or field stars in the Milky Way disc, bulge, and halo. Conclusions. The GES dataset of homogeneous lithium abundances described here will be valuable for our understanding of several processes, from stellar evolution and internal mixing in stars at different evolutionary stages to Galactic evolution. © E. Franciosini et al. 2022., Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programmes 188.B-3002, 193.B-0936, and 197.B-1074. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofísico di Arcetri. These data have been obtained from the Gaia-ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) in the form of the grant “Premíale VLT 2012”. The results presented here benefit from discussions held during the Gaia-ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. We acknowledge the support from INAF in the form of the grant for mainstream projects “Enhancing the legacy of the Gaia-ESO Survey for open clusters science”. R.S. acknowledges support from the National Science Centre, Poland (2014/15/B/ST9/03981). T.B. was supported by grant no. 2018-04857 from the Swedish Research Council. M.B. is supported through the Lise Meitner grant from the Max Planck Society. We acknowledge support by the Collaborative Research centre SFB 881 (projects A5, A10), Heidelberg University, of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 949173). This work made use of Astropy (http://www.astropy.org), a community-developed core Python package for Astronomy (Astropy Collaboration 2013, 2018)., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.