We combine experimental observations with ab initio calculations to study the reversible hydrogenation of single-wall carbon nanotubes using high boiling polyamines as hydrogenation reagents. Our calculations characterize the nature of the adsorption bond and identify preferential adsorption geometries at different coverages. We find the barrier for sigmatropic rearrangement of chemisorbed hydrogen atoms to be similar to 1 eV, thus facilitating surface diffusion and formation of energetically favored, axially aligned adsorbate chains. Chemisorbed hydrogen modifies the structure and stability of nanotubes significantly and increases the inter-tube distance, thus explaining the improved dispersability in solvents like methanol, ethanol, chloroform, and benzene.