We present a comprehensive study of the morphological properties of 42 gamma-ray burst (GRB) host galaxies imaged with the Hubble Space Telescope in the optical band. The purpose of this study is to understand the relation of GRBs to their macro-environments, and to compare the GRB-selected galaxies to other high redshift samples. We perform both qualitative and quantitative analyses by categorizing the galaxies according to their visual properties, and by examining their surface brightness profiles. We find that all of the galaxies have approximately exponential profiles, indicative of galactic disks, and have a median scale length of about 1.7 kpc. Inspection of the visual morphologies reveals a high fraction of merging and interacting systems, with ~30% showing clear signs of interaction, and an additional ~30% exhibiting irregular and asymmetric structure which may be the result of recent mergers; these fractions are independent of redshift and galaxy luminosity. On the other hand, the three GRB host galaxies for which submillimeter and radio emission has been detected are isolated and compact, unlike the luminous submillimeter-selected galaxies. The fraction of mergers appears to be elevated compared to other high redshift samples, particularly for the low luminosities of GRB hosts (M_B ~ -16 to -21 mag). This suggests that merging and interacting galaxies undergoing a burst of star formation may be an efficient site for the production of GRB progenitors. Finally, we show that GRB hosts clearly follow the size-luminosity relation present in other galaxy samples, but thanks to absorption redshifts they help extend this relation to lower luminosities.
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