  We report on the stellar content, half-light radii and star formation rates
of a sample of 10 known high-redshift ($z\gtrsim 2$) galaxies selected on
strong neutral hydrogen (HI) absorption (log(N(HI)/cm$^{-2})>19$) toward
background quasars. We use observations from the {\it Hubble Space Telescope}
(HST) Wide Field Camera 3 in three broad-band filters to study the spectral
energy distribution(SED) of the galaxies. Using careful quasar point spread
function subtraction, we study their galactic environments, and perform the
first systematic morphological characterisation of such absorption-selected
galaxies at high redshifts. Our analysis reveals complex, irregular hosts with
multiple star-forming clumps. At a spatial sampling of 0.067 arcsec per pixel
(corresponding to 0.55 kpc at the median redshift of our sample), 40% of our
sample requires multiple S\'ersic components for an accurate modelling of the
observed light distributions. Placed on the mass-size relation and the `main
sequence' of star-forming galaxies, we find that absorption-selected galaxies
at high redshift extend known relations determined from deep
luminosity-selected surveys to an order of magnitude lower stellar mass, with
objects primarily composed of star-forming, late-type galaxies. We measure
half-light radii in the range $r_{1/2} \sim$ 0.4 to 2.6 kpc based on the
reddest band (F160W) to trace the oldest stellar populations, and stellar
masses in the range $\log (\mathrm{M}_{\star}/\mathrm{M}_{\odot}) \sim$ 8 to 10
derived from fits to the broad-band SED. Spectroscopic and SED-based star
formation rates are broadly consistent, and lie in the range log(SFR/M$_{\odot}
$yr$^{-1}$) $\sim$0.0 to 1.7.
