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The second data release of the LOFAR Two-Metre Sky Survey (LoTSS) covers 27%of the northern sky, with a total area of $\sim 5,700$ deg$^2$. The highangular resolution of LOFAR with Dutch baselines (6 arcsec) allows us to carryout optical identifications of a large fraction of the detected radio sourceswithout further radio followup; however, the process is made more challengingby the many extended radio sources found in LOFAR images as a result of itsexcellent sensitivity to extended structure. In this paper we present sourceassociations and identifications for sources in the second data release basedon optical and near-infrared data, using a combination of a likelihood-ratiocross-match method developed for our first data release, our citizen scienceproject Radio Galaxy Zoo: LOFAR, and new approaches to algorithmic opticalidentification, together with extensive visual inspection by astronomers. Wealso present spectroscopic or photometric redshifts for a large fraction of theoptical identifications. In total 4,116,934 radio sources lie in the area withgood optical data, of which 85% have an optical or infrared identification and58% have a good redshift estimate. We demonstrate the quality of the dataset bycomparing it with earlier optically identified radio surveys. This is by farthe largest ever optically identified radio catalogue, and will permit robuststatistical studies of star-forming and radio-loud active galaxies.

The LOFAR Two-Metre Sky Survey (LoTSS): VI. Optical identifications for the second data release