Covalent addition of functional groups onto carbon nanotubes is known to generate lattice point defects that disrupt the electronic wave function, resulting namely in a reduction of their optical response and electrical conductance. Here, conductance measurements combined with numerical simulations are used to unambiguously identify the presence of graft-induced midgap states in the electronic structure of covalently functionalized semiconducting carbon nanotubes. The main experimental evidence is an increase of the conductance in the OFF-state after covalent addition of 4-bromophenyl grafts on many single- and double-walled individual nanotubes, the effect of which is fully suppressed after thermodesorption of the adducts. The graft-induced current leakage is thermally activated and can reach several orders of magnitude above its highly insulating pristine-state level. Ab initio simulations of various configurations of functionalized nanotubes corroborate the presence of these midgap states and show their localization around the addends. Moreover, the electronic density of these localized states exhibits an extended hydrogenoid profile along the nanotube axis, providing access for long-range coupling between the grafts. We argue that covalent nanotube chemistry is a powerful tool to prepare and control midgap electronic states on nanotubes for enabling further studies of the intriguing properties of interacting 1D localized states.