Conventional chemotherapeutic approaches currently used for brain tumor treatment have low efficiency in targeted drug delivery and often have non-target toxicity. Development of stable and effective drug delivery vehicles for the most incurable diseases is one of the urgent biomedical challenges. We have developed polymer nanoparticles (NPs) with improved temozolomide (TMZ) delivery for promising brain tumor therapy, performing a rational design of polyelectrolyte complexes of oppositely charged polysaccharides of cationic chitosan and anionic pectin. The NPs’ diameter (30 to 330 nm) and zeta-potential (−29 to 73 mV) varied according to the initial mass ratios of the biopolymers. The evaluation of nanomechanical parameters of native NPs demonstrated changes in Young’s modulus from 58 to 234 kPa and adhesion from −0.3 to −3.57 pN. Possible mechanisms of NPs’ formation preliminary based on ionic interactions between ionogenic functional groups were proposed by IR spectroscopy and dynamic rheology. The study of the parameters and kinetics of TMZ sorption made it possible to identify compounds that most effectively immobilize and release the active substance in model liquids that simulate the internal environment of the body. A polyelectrolyte carrier based on an equal ratio of pectin–chitosan (0.1% by weight) was selected as the most effective for the delivery of TMZ among a series of obtained NPs, which indicates a promising approach to the treatment of brain tumors.