We report measurements of hydrogen desorption and its effect on the magnetism of pseudomorphic ultrathin films of Fe, Co, and Ni on Cu (001). Hydrogen desorption is measured with thermal desorption spectroscopy (TDS) and changes in the magnetic properties with saturation hydrogen coverage are measured with the surface magneto-optic Kerr effect (SMOKE). TDS of hydrogen shows that Co films less than 2.5 monolayers thick do not completely cover the substrate, and that Co deposited at 300 K does not alloy with the Cu(001) substrate. By carefully controlling the thickness of the Ni films, we can tune the ferromagnetic Curie temperature to below the hydrogen desorption temperature. The thermal desorption of hydrogen from the paramagnetic Ni thin film surface is similar to that from bulk ferromagnetic Ni(001) indicating magnetism has no measurable effect on thermal desorption kinetics. Hydrogen is more weakly chemisorbed on ferromagnetic Co thin film surfaces and more strongly chemisorbed on ferromagnetic Fe thin film surfaces as compared to Ni(001). SMOKE measurements show hydrogen chemisorption produces a magnetically ''dead'' surface layer on Ni films, a reduction in the surface layer magnetism on Co films, and an enhancement in the surface layer magnetism on Fe films.