Cerium oxide nanoparticles (CeO₂ NPs) are well known for their application in various fields of industry, as well as in biology and medicine. Knowledge of synthesis schemes, physicochemical and morphological features of nanoscale CeO₂ is important for assessing their antioxidant behavior and understanding the mechanism of oxidative stress and its consequences. The choice of the method of synthesis should be based on the possibility to choose the conditions and parameters for obtaining CeO₂ with controlled dimensions and a ratio of Се³⁺/Се⁴⁺ on their surface. In this study, CeO₂ NPs are synthesized by precipitation in mixed water-alcohol solutions at constant pH=9. The properties of obtained NPs are studied using various methods of physical-chemical characterization such as X-ray diffraction, X-ray photoelectron spectroscopy, transmission electron microscopy, and dynamic light scattering. The size of CeO₂ NPs varied from 14 to 4.2 nm with increasing alcohol concentration, while the effect of constant pH during synthesis on the morphology of the particles was insignificant. The synthesized nanoparticles form highly stable aqueous suspensions since their zeta-potential is higher than +40 mV. It is found that the ability of CeO₂ NPs to self-stabilize is associated with the presence of hydrated Ce⁴⁺ ions on their surface. In vitro biological studies have shown that, regardless of particle size, CeO₂ NPs have antioxidant potential, but smaller NPs with a higher percentage of Ce³⁺ on the surface had a more effective antioxidant effect. In addition, the size-depended activity of CeO₂ NPs to inhibit the amyloid formation of insulin is demonstrated.