A novel type of copper-based regulating agents was first applied in radical polymerization of methyl methacrylate and acrylonitrile. It was shown that systems based on copper complex with redox-active bis(acetonaphthene) ligand (dpp-BIAN↔CuCl)2, carbon tetrachloride and different activating agents such as ascorbic acid or amines (tert-butylamine, diethylamine, triethylamine and pyridine) were capable to initiate polymerization of the above monomers in wide temperature range from 25 to 110 °C. The amine structure and basicity were found to make great impact on polymerization and molecular weight parameters of the obtained products. The systems developed are capable of conducting polymerization up to high monomer conversions in a wide temperature range leading to polymers with rather low molecular weight and moderate polydispersity. The most efficient system in terms of controlling the molecular weight characteristics of poly(methyl methacrylate) among others is the system based on (dpp-BIAN↔CuCl)2 and diethylamine, which makes it possible to obtain polymer with a polydispersity index of 1.36–1.60. In case of acrylonitrile polymerization, the highest polymer yield is achieved using a copper complex and triethylamine. The results of MALDI TOF mass spectroscopy measurements showed the presence of chlorine atoms at the chain ends of macromolecules. The formation of “living” chains during polymerization of methyl methacrylate was confirmed by the synthesis of block-copolymers with styrene.