Novel hybrid magnetoactive composite scaffolds based on poly(3-hydroxybutyrate) (PHB), gelatin, and magnetite (Fe3O4) were fabricated by electrospinning. The morphology, structure, phase composition, and magnetic properties of composite scaffolds were studied. Fabrication procedures of PHB/gelatin and PHB/gelatin/Fe3O4 scaffolds resulted in the formation of both core-shell and ribbon-shaped structure of the fibers. In case of hybrid PHB/gelatin/Fe3O4 scaffolds submicron-sized Fe3O4 particles were observed in the surface layers of the fibers. The X-ray photoelectron spectroscopy results allowed the presence of gelatin on the fiber surface (N/C ratio–0.11) to be revealed. Incubation of the composite scaffolds in saline for 3 h decreased the amount of gelatin on the surface by more than ~75%. The differential scanning calorimetry results obtained for pure PHB scaffolds revealed a characteristic melting peak at 177.5 °C. The presence of gelatin in PHB/gelatin and PHB/gelatin/Fe3O4 scaffolds resulted in the decrease in melting temperature to 168–169 °C in comparison with pure PHB scaffolds due to the core-shell structure of the fibers. Hybrid scaffolds also demonstrated a decrease in crystallinity from 52.3% (PHB) to 16.9% (PHB/gelatin) and 9.2% (PHB/gelatin/Fe3O4). All the prepared scaffolds were non-toxic and saturation magnetization of the composite scaffolds with magnetite was 3.27 ± 0.22 emu/g, which makes them prospective candidates for usage in biomedical applications.