Silver nanoparticles (AgNPs) with broad-spectrum antimicrobial properties are gaining increasing interest in fighting multidrug-resistant bacteria. Herein, we describe the synthesis of AgNPs, stabilized by polyvinyl alcohol (PVA), with high purity and homogeneous sizes, using radiolysis. Solvated electrons and reducing radicals are induced from solvent radiolysis and no other chemical reducing agents are needed to reduce the metal ions. Another advantage of this method is that it leads to sterile colloidal suspensions, which can be directly used for medical applications. We systematically investigated the effect of the silver salt precursor on the optical properties, particle size, and morphology of the resulting colloidal AgNPs. With Ag2SO4 precursor, the AgNPs displayed a narrow size distribution (20 ± 2 nm). In contrast, AgNO3 and AgClO4 precursors lead to inhomogeneous AgNPs of various shapes. Moreover, the optimized AgNPs synthesized from Ag2SO4 were stable upon storage in water and phosphate-buffered saline (PBS) and were very effective in inhibiting the growth of Staphylococcus aureus (S. aureus) at a concentration of 0.6 μg·mL−1 while completely eradicating it at a concentration of 5.6 μg·mL−1. When compared with other AgNPs prepared by other strategies, the remarkable bactericidal ability against S. aureus of the AgNPs produced here opens up new perspectives for further applications in medicine, cosmetics, the food industry, or in elaborating antibacterial surfaces and other devices.