In this work, by using water steam only, two antioxidant extracts were obtained from olive leaves (Olea europaea L.), a by-product of olive oil chain. Olive leaf extracts (OLEs) were tested as such (water extract: WE) and partially purified with ethyl acetate (ethyl acetate [EA] extract). Total phenols were 7.4 mg/mL and 3.8 mg/mL in WE and EA final solutions, respectively, evidencing a different composition by high-performance liquid chromatography analysis. Both extracts were evaluated in vitro in comparison to pure hydroxytyrosol (Hy). A 2,2-diphenyl-1-picrylhydrazyl (DPPH) EC50 of 57.6, 76.5, and 39.7 µg/mL and a ferric reducing antioxidant power EC50 of 84.8, 69.9, 41.2 µg/mL were determined for WE, EA, and Hy solution, respectively. The Rancimat induction time determined at 120°C in a lard sample with 200-ppm total phenol equivalent addition of WE, EA, and Hy was 8.92 h, 12.74 h, and 7.27 h, respectively (vs. 2.24 h for lard only). Extracts were added at the same dose (200 ppm) to minced beef patties that were put in closed containers under controlled air headspace composition (NA, natural air; HOA, modified air with 80% O2; and 20% N2) and stored at 4°C up to 10 days. Extracts showed significant effectiveness in contrasting decrease of O2 level in containers as well as pH and color changes of patties. A significant increase (expressed as mg of malondialdehyde MDA/kg; thiobarbituric acid-reactive substance (TBARS) assay was conducted in control samples at an interval of 0–10 days (from 0.52 to 0.78 mg of MDA/kg in NA samples; and from 0.55 to 1.31 mg of MDA/kg in HOA samples), while minimal changes were observed in treated samples. These findings suggest a potential use of OLEs for maintaining quality and oxidative stability of beef patties during storage.