Polymer gel electrolytes (PGE) belonging to salt–solvent–polymer hybrid systems are prepared using a mixture of lithium bis(oxalato)borate (LiBOB), γ-butyrolactone (γ-BL), and cellulose acetate (CA). The increase in ionic conductivity of PGE is due to the dissociation of ion aggregates, as confirmed by Fourier transform infrared analysis. The highest conductivity attained by the PGE is 7.05 mS cm−1 at 2.4 wt.% CA. The plots of conductivity–temperature show a classical Arrhenius relationship. The electrical properties of the sample with the highest conductivity are analyzed using electrical permittivity and electric modulus formalism studies. Meanwhile, the frequency-dependent conductivity of the polymer gel electrolyte adheres to Jonscher’s power law. Conduction mechanism study also shows that the 2.4 wt.% CA PGE is in agreement with the small polaron hopping model.