This study originally explores the use of naringin (NAR), gallic acid (GA), caffeic acid (CA), and quercetin (QUER) as natural antioxidants for bio-based high-density polyethylene (bio-HDPE). These phenolic compounds are present in various citrus fruits and grapes and can remain in their leaves, peels, pulp, and seeds as by-products or wastes after juice processing. Each natural additive was first melt-mixed at 0.8 parts per hundred resin (phr) of bio-HDPE by extrusion and the resultant pellets were shaped into films by thermo-compression. Although all the phenolic compounds colored the bio-HDPE films, their contact transparency was still preserved. The chemical analyses confirmed the successful inclusion of the phenolic compounds in bio-HDPE, though their interaction with the green polyolefin matrix was low. The mechanical performance of the bio-HDPE films was nearly unaffected by the natural compounds, presenting in all cases a ductile behavior. Interestingly, the phenolic compounds successfully increased the thermo-oxidative stability of bio-HDPE, yielding GA and QUER the highest performance. In particular, using these phenolic compounds, the onset oxidation temperature (OOT) value was improved by 43 and 41.5 °C, respectively. Similarly, the oxidation induction time (OIT) value, determined in isothermal conditions at 210 °C, increased from 4.5 min to approximately 109 and 138 min. Furthermore, the onset degradation temperature in air of bio-HDPE, measured for the 5% of mass loss (T5%), was improved by up to 21 °C after the addition of NAR. Moreover, the GA- and CA-containing bio-HDPE films showed a high antioxidant activity in alcoholic solution due to their favored release capacity, which opens up novel opportunities in active food packaging. The improved antioxidant performance of these phenolic compounds was ascribed to the multiple presence of hydroxyl groups and aromatic heterocyclic rings that provide these molecules with the features to permit the delocalization and the scavenging of free radicals. Therefore, the here-tested phenolic compounds, in particular QUER, can represent a sustainable and cost-effective alternative of synthetic antioxidants in polymer and biopolymer formulations, for which safety and environmental issues have been raised over time.