In the present study, alginate–silver nanoparticle (Alg-AgNP) nanocomposite hydrogels possessing antibacterial activity were synthesized via an innovative route. A task-specific designed Natural Deep Eutectic Solvent (NADES), composed of glucose, lactic acid, and water, was utilized as a green extraction solvent of bioactive compounds from olive leaves (OLs). The NADES–olive leaf extract (NADES-OLE) was used as obtained for the preparation of the Alg-AgNP nanocomposite hydrogel as a multiple-role component. The NADES-OLE acts (a) as a crosslinking agent for the preparation of the alginate hydrogels, (b) as a reducing agent for the in situ synthesis of AgNPs during hydrogel formation, and (c) as a bioactivity enhancement agent due to the presence of compounds obtained from the olive leaves. The Alg-AgNP hydrogel preparation process was optimized through a Box–Behnken experimental design. The resulting nanocomposite hydrogels were characterized for their swelling capacity and water retention in phosphate buffer (pH 5.5), achieving 538% swelling capacity within 180 min and 90% water retention after 250 min. The AgNPs formed within the hydrogels were found to have an average size of 103.2 ± 5.6 nm, with a concentration of 1.2 10⁸ ± 2.2 ∗ 10⁷ particles/mL. Antibacterial testing of the nanocomposite hydrogels against foodborne pathogens, including Gram-negative (Escherichia coli, Salmonella Typhimurium, Yersinia enterocolitica) and Gram-positive bacteria (Listeria monocytogenes, Staphylococcus aureus, Bacillus cereus), revealed significant antibacterial activity, particularly against E. coli (64.9%), Y. enterocolitica (60.6%), S. aureus (79.1%), and B. cereus (55.3%), at a concentration of 1 mg/mL.