Hydrogen adatoms are shown to generate magnetic moments inside single layer graphene. Spin transport measurements on graphene spin valves exhibit a dip in the nonlocal spin signal as a function of the applied magnetic field, which is due to scattering (relaxation) of pure spin currents by exchange coupling to the magnetic moments. Furthermore, Hanle spin precession measurements indicate the presence of an exchange field generated by the magnetic moments. The entire experiment including spin transport is performed in an ultrahigh vacuum chamber, and the characteristic signatures of magnetic moment formation appear only after hydrogen adatoms are introduced. Lattice vacancies also demonstrate similar behavior indicating that the magnetic moment formation originates from p(z)-orbital defects.