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We report on the stellar content, half-light radii and star formation ratesof a sample of 10 known high-redshift ($z\gtrsim 2$) galaxies selected onstrong neutral hydrogen (HI) absorption (log(N(HI)/cm$^{-2})>19$) towardbackground quasars. We use observations from the {\it Hubble Space Telescope}(HST) Wide Field Camera 3 in three broad-band filters to study the spectralenergy distribution(SED) of the galaxies. Using careful quasar point spreadfunction subtraction, we study their galactic environments, and perform thefirst systematic morphological characterisation of such absorption-selectedgalaxies at high redshifts. Our analysis reveals complex, irregular hosts withmultiple 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 oursample requires multiple S\'ersic components for an accurate modelling of theobserved light distributions. Placed on the mass-size relation and the `mainsequence' of star-forming galaxies, we find that absorption-selected galaxiesat high redshift extend known relations determined from deepluminosity-selected surveys to an order of magnitude lower stellar mass, withobjects primarily composed of star-forming, late-type galaxies. We measurehalf-light radii in the range $r_{1/2} \sim$ 0.4 to 2.6 kpc based on thereddest band (F160W) to trace the oldest stellar populations, and stellarmasses in the range $\log (\mathrm{M}_{\star}/\mathrm{M}_{\odot}) \sim$ 8 to 10derived from fits to the broad-band SED. Spectroscopic and SED-based starformation rates are broadly consistent, and lie in the range log(SFR/M$_{\odot}$yr$^{-1}$) $\sim$0.0 to 1.7.

Absorption-selected galaxies trace the low-mass, late-type, star-forming population at $z\sim2-3$