The LOFAR Two-metre Sky Survey (LoTSS) is an ongoing sensitive, high-resolution 120-168 MHz survey of the Northern sky with diverse and ambitious science goals. Many of the scientific objectives of LoTSS rely upon, or are enhanced by, the association or separation of the sometimes incorrectly catalogued radio components into distinct radio sources, and the identification and characterisation of the optical counterparts to these sources. Here we present the source associations and optical and/or IR identifications for sources in the first data release, which are made using a combination of statistical techniques and visual association and identification. We document in detail the colour- and magnitude-dependent likelihood ratio method used for statistical identification as well as the Zooniverse project, called LOFAR Galaxy Zoo, used for the visual classification. We describe the process used to select which of these two different methods is most appropriate for each LoTSS source. The final LoTSS-DR1-IDs value-added catalogue presented contains 318,520 radio sources, of which 231,716 (73%) have optical and/or IR identifications in Pan-STARRS and WISE. The value-added catalogue is available online at https://lofar-surveys.org/, as part of this data release.