Developing biodegradable materials based on polymer blends with a programmable self-destruction period in the environmental conditions of living systems is a promising direction in polymer chemistry. In this work, novel non-woven fibrous materials obtained by electrospinning based on the blends of poly(lactic acid) (PLA) and poly(3-hydroxybutyrate) (PHB) were developed. The kinetics of biodegradation was studied in the aquatic environment of the inoculum of soil microorganisms. Oxidative degradation was studied under the ozone gaseous medium. The changes in chemical composition and structure of the materials were studied by optical microscopy, DSC, TGA, and FTIR-spectroscopy. The disappearance of the structural bands of PHB in the IR-spectra of the blends and a significant decrease in the enthalpy of melting after 90 days of exposure in the inoculum indicated the biodegradation of PHB while PLA remained stable. It was shown that the rate of ozonation was higher for PLA and the blends with a high content of PLA. The lower density of the amorphous regions of the blends determined an increased rate of their oxidation by ozone compared to homopolymers. The optimal composition in terms of degradation kinetics is a fibrous material based on the blend of 30PLA/70PHB that can be used as an effective ecosorbent, for biopackaging, and as a highly porous covering material for agricultural purposes.