Agri-food industry wastes and by-products include highly valuable components that can upgraded, providing low-cost bioactives or used as an alternative protein source. In this context, by-products from olive production and olive oil extraction process, i.e., seeds, can be fostered. In particular, this work was aimed at extracting and characterizing proteins for Olea europaea L. seeds and at producing two protein hydrolysates using alcalase and papain, respectively. Peptidomic analysis were performed, allowing to determine both medium- and short-sized peptides and to identify their potential biological activities. Moreover, an extensive characterization of the antioxidant properties of Olea europaea L. seed hydrolysates was carried out both in vitro by 2,2-diphenyl-1-picrylhydrazyl (DPPH), by ferric reducing antioxidant power (FRAP), and by 2,2′-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS) assays, respectively, and at cellular level by measuring the ability of these hydrolysates to significant reduce the H2O2-induced reactive oxygen species (ROS) and lipid peroxidation levels in human intestinal Caco-2 cells. The results of the both hydrolysates showed significant antioxidant properties by reducing the free radical scavenging activities up to 65.0 ± 0.1% for the sample hydrolyzed with alcalase and up to 75.7 ± 0.4% for the papain hydrolysates tested at 5 mg/mL, respectively. Moreover, similar values were obtained by the ABTS assays, whereas the FRAP increased up to 13,025.0 ± 241.5% for the alcalase hydrolysates and up to 12,462.5 ± 311.9% for the papain hydrolysates, both tested at 1 mg/mL. According to the in vitro results, both papain and alcalase hydrolysates restore the cellular ROS levels up 130.4 ± 4.24% and 128.5 ± 3.60%, respectively, at 0.1 mg/mL and reduce the lipid peroxidation levels up to 109.2 ± 7.95% and 73.0 ± 7.64%, respectively, at 1.0 mg/mL. In addition, results underlined that the same hydrolysates reduced the activity of dipeptidyl peptidase-IV (DPP-IV) in vitro and at cellular levels up to 42.9 ± 6.5% and 38.7 ± 7.2% at 5.0 mg/mL for alcalase and papain hydrolysates, respectively. Interestingly, they stimulate the release and stability of glucagon-like peptide 1 (GLP-1) hormone through an increase of its levels up to 660.7 ± 21.9 pM and 613.4 ± 39.1 pM for alcalase and papain hydrolysates, respectively. Based on these results, olive seed hydrolysates may represent new ingredients with antioxidant and anti-diabetic properties for the development of nutraceuticals and functional foods for the prevention of metabolic syndrome onset.