This work reports on a novel polyester copolymer containing poly(dopamine), a synthetic analogue of natural melanin, evaluated in a sustained-release drug delivery system for ocular intravitreal administration of drugs. More specifically, a graft copolymer of poly(ε-caprolactone)-graft-poly(dopamine) (PCL-g-PDA) has been synthesized and was shown to further extend the drug release benefits of state-of-the-art biodegradable intravitreal implants composed of poly(lactide) and poly(lactide-co-glycolide). The innovative biomaterial combines the documented drug-binding properties of melanin naturally present in the eye, with the established ocular tolerability and biodegradation of polyester implants. The PCL-g-PDA copolymer was obtained by a two-step modification of PCL with a final PDA content of around 2-3 wt % and was fully characterized by size exclusion chromatography, NMR, and diffusion ordered NMR spectroscopy. The thermoplastic nature of PCL-g-PDA allowed its simple processing by hot-melt compression molding to prepare small implants. The properties of unmodified PCL and PCL-g-PDA implants were studied and compared in terms of thermal properties (differential scanning calorimetry), thermal stability (thermogravimetry analysis), degradability, and in vitro cytotoxicity. PCL and PCL-g-PDA implants exhibited similar degradation properties in vitro and were both stable under physiological conditions over 110 days. Likewise, both materials were non-cytotoxic toward L929 and ARPE-19 cells. The drug loading and in vitro release properties of the new materials were investigated with dexamethasone (DEX) and ciprofloxacin hydrochloride (CIP) as representative drugs featuring low and high melanin-binding affinities, respectively. In comparison to unmodified PCL, PCL-g-PDA implants showed a significant extension of drug release, most likely because of specific drug-catechol interaction with the PDA moieties of the copolymer. The present study confirms the advantages of designing PDA-containing polyesters as a class of biodegradable and biocompatible thermoplastics that can modulate and remarkably extend the drug release kinetics thanks to their unique drug-binding properties, especially, but not limited to, for ocular applications.