Curcumin is a natural polyphenol that exhibits remarkable antioxidant and anti-inflammatory activities; however, its clinical application is limited in part by its physiological instability. Here, we report the synthesis of curcumin-derived polyesters that release curcumin upon hydrolytic degradation to improve curcumin stability and solubility in physiological conditions. Curcumin was incorporated in the polymer backbone by a one-pot condensation polymerization in the presence of sebacoyl chloride and polyethylene glycol (PEG, Mn = 1 kDa). The thermal and mechanical properties, surface wettability, self-assembly behavior, and drug-release kinetics all depend sensitively on the mole percentage of curcumin incorporated in these statistical copolymers. Curcumin release was triggered by the hydrolysis of phenolic esters on the polymer backbone, which was confirmed using a PEGylated curcumin model compound, which represented a putative repeating unit within the polymer. The release rate of curcumin was controlled by the hydrophilicity of the polymers. Burst release (2 days) and extended release (>8 weeks) can be achieved from the same polymer depending on curcumin content in the copolymer. The materials can quench free radicals for at least 8 weeks and protect primary neurons from oxidative stress in vitro. Further, these copolymer materials could be processed into both thin films and self-assembled particles, depending on the solvent-based casting conditions. Finally, we envision that these materials may have potential for neural tissue engineering application, where antioxidant release can mitigate oxidative stress and the inflammatory response following neural injury.