The LOFAR Two-metre Sky Survey ( LoTSS ) is a sensitive , high-resolution 120-168 MHz survey of the Northern sky . The LoTSS First Data Release ( DR1 ) presents 424 square degrees of radio continuum observations over the HETDEX Spring Field ( 10h45m00s < right ascension < 15h30m00s and 45 ^ { \circ } 00 \arcmin 00 \arcsec < declination < 57 ^ { \circ } 00 \arcmin 00 \arcsec ) with a median sensitivity of 71 \mu Jy/beam and a resolution of 6 \arcsec . In this paper we present photometric redshifts ( photo- z ) for 94.4 % of optical sources over this region that are detected in the Panoramic Survey Telescope and Rapid Response System ( Pan-STARRS ) 3 \pi steradian survey . Combining the Pan-STARRS optical data with mid-infrared photometry from the Wide-field Infrared Survey Explorer , we estimate photo- z s using a novel hybrid photometric redshift methodology optimised to produce the best possible performance for the diverse sample of radio continuum selected sources . For the radio-continuum detected population , we find an overall scatter in the photo- z of 3.9 % and an outlier fraction ( \left|z _ { \textup { phot } } - z _ { \textup { spec } } \right| / ( 1 + z _ { \text { spec } } ) > 0.15 ) of 7.9 \% . We also find that , at a given redshift , there is no strong trend in photo- z quality as a function of radio luminosity . However there are strong trends as a function of redshift for a given radio luminosity , a result of selection effects in the spectroscopic sample and/or intrinsic evolution within the radio source population . Additionally , for the sample of sources in the LoTSS First Data Release with optical counterparts , we present rest-frame optical and mid-infrared magnitudes based on template fits to the consensus photometric ( or spectroscopic when available ) redshift .