We have found the atomic gas (HI) reservoirs of the blue ultra diffuse galaxy (UDG) candidates identified by Roman and Trujillo in images near Hickson Compact Groups (HCGs). We confirm that all of the objects are indeed UDGs with effective radii R_e > 1.5 kpc. Three of them are likely to be gravitationally bound to the HCG near which they project, one is plausibly gravitationally bound to the nearest HCG, and one is in the background. We measure HI masses and velocity widths for each object directly from the spectra, and use the widths together with the UDG effective radii to estimate dynamical masses and halo spin parameters. The location of the blue UDGs in the HI mass - stellar mass plane is consistent with that of the broader gas-rich galaxy population, and both their HI masses and gas richnesses are correlated with their effective radii. The blue UDGs appear to be low-mass objects with high-spin halos, although their properties are not as extreme as those of the faintest diffuse objects found in HI searches. The data presented here highlight the potential of single-dish radio observations for measuring the physical properties of blue diffuse objects detected in the optical.