  The Low Frequency Array (LOFAR) Two-metre Sky Survey (LoTSS) is a sensitive,
high-resolution 120-168 MHz survey split across multiple tiers over the
northern sky. The first LoTSS Deep Fields data release consists of deep radio
continuum imaging at 150 MHz of the Bo\"{o}tes, European Large Area Infrared
Space Observatory Survey-North 1 (ELAIS-N1), and Lockman Hole fields, down to
rms sensitivities of $\sim$32, 20, and 22 $\mu$Jy beam$^{-1}$, respectively. In
this paper we present consistent photometric redshift (photo-$z$) estimates for
the optical source catalogues in all three fields - totalling over 7 million
sources ($\sim5$ million after limiting to regions with the best photometric
coverage). Our photo-$z$ estimation uses a hybrid methodology that combines
template fitting and machine learning and is optimised to produce the best
possible performance for the radio continuum selected sources and the wider
optical source population. Comparing our results with spectroscopic redshift
samples, we find a robust scatter ranging from 1.6 to 2% for galaxies and 6.4
to 7% for identified optical, infrared, or X-ray selected active galactic
nuclei (AGN). Our estimated outlier fractions ($\left | z_{\text{phot}} -
z_{\text{spec}} \right | / (1+z_{\text{spec}}) > 0.15$) for the corresponding
subsets range from 1.5 to 1.8% and 18 to 22%, respectively. Replicating trends
seen in analyses of previous wide-area radio surveys, we find no strong trend
in photo-$z$ quality as a function of radio luminosity for a fixed redshift. We
exploit the broad wavelength coverage available within each field to produce
galaxy stellar mass estimates for all optical sources at $z < 1.5$. Stellar
mass functions derived for each field are used to validate our mass estimates,
with the resulting estimates in good agreement between each field and with
published results from the literature.
