It has been established for the first time that cationic polymerization of butadiene in the presence of the initiating system diethylaluminum chloride—allyl chloride allows the synthesis of fully soluble solid thermoplastic polymers with reduced unsaturation (40–48 mol.% of theoretical) and high glass transition (56–65 °C) and softening point (126–193 °C) temperatures. The structure of the synthesized polybutadiene macromolecules, including the structure of the head units consisting of allyl fragments of the polymerization initiator (allyl chloride) connected with the 1,4-trans-unit of polybutadiene, has been determined. The resulting polymers may find a practical application in the production of adhesive and sealing compositions.