Thermoplastic elastomers (TPEs) are materials combining the processability of thermoplastics and the elasticity of rubbers. The global value and demand of TPEs are expected to grow in the coming years, and advancement in synthetic chemistry is the key driving force. This contribution provides a simple synthesis of high-ethylene EPDMs with high molecular weight, narrow molecular weight distribution (1.9 < Mw/Mn < 2.3), and properties which can be adjusted from soft thermoplastic to elastomer. EPDMs are prepared through the terpolymerization of ethylene with propylene and 5-ethylidene-2-norbornene (ENB), where ethylene is continuously supplied to the reaction bath, while propylene and ENB are added only at the beginning. Polymerizations are catalyzed by three known imido vanadium(IV) complexes, differing in the imido substituent and coligand, in combination with Et2AlCl and Cl3CCO2Et. The obtained EPDMs are a mixture of macromolecules, each of them featuring a nonrandom comonomer distribution and nonuniform composition. Each chain likely contains multiblocks where the comonomers are segmented, i.e., blocks with high ethylene content that may crystallize and blocks with high propylene and ENB content that may not crystallize. This broad chemical composition distribution is due to time drift that occurs during the polymerization, which in turn depends on the experimental conditions and ligand set. Composition drift causes variation in the instantaneous feed comonomer ratio and hence in the chemical composition of the terpolymer over the period of conversion. In proper experimental conditions, EPDMs behave as TPEs without the need of vulcanization, polymer blending, and reinforcement through the addition of fillers. They exhibit high elongation at break, strain hardening at large deformation, remarkable shape retention properties (up to 76% recovery after 10 cycles at 300% and about 90% at 410% strain), and remelting processability with no fall in properties for recycle and reuse.