The controlled radical polymerization of N,N-dimethylamino-2-ethyl methacrylate on polyimide multicenter macroinitiators under the action of the activating complex of Cu(I) with nitrogen-containing ligands is studied. The complex investigation of the kinetics of copolymerization and the molecular-mass characteristics of the products is performed. The polarity of a medium and the nature of the nitrogen-containing ligand used to prepare the catalytic complex considerably affect the rate of polymerization and the composition and molecular-mass characteristics of the product. Process conditions that enable the synthesis of regularly graft copolyimides with poly(N,N-dimethylamino-2-ethyl methacrylate) side chains are determined. It is shown that the products of grafting copolymerization may be used as a nanoreactor and a stabilizing agent for the template synthesis of composite structures containing silver nanoparticles in the absence of additional reducing agents.