Innovative fibrous materials from cellulose derivative, cellulose acetate (CA) and water-soluble polyether, polyethylene glycol (PEG) loaded with natural biologically active compounds (BAC), quercetin (QUE) and rutin (RUT), have been successfully fabricated by blend electrospinning and dual electrospinning. Scanning electron microscopy revealed that the mean fiber diameters of all the obtained fibers were in the nanometer range. QUE and RUT incorporated in the fibrous mats were in the amorphous state, as evidenced by the performed differential scanning calorimetry (DSC) and X-ray diffraction (XRD) analysis. The presence of the polyether in the developed fibrous material assisted the in vitro release of the biologically active compounds by improving the hydrophilicity and wettability of the mats. Rutin-containing fibrous materials manifest the highest antioxidative activity, as determined by the 2,2-diphenyl-1-picryl-hydrazyl-hydrate free radical method. The cytotoxicity of the fabricated novel materials was evaluated using a tumor cell line and normal mouse fibroblast cells. The mats containing QUE and QUE/RUT independent of the applied spinning method show a higher cytotoxic effect against cancer cells and 3 to 4.5 times lower cytotoxicity to a noncancer cell line. These features make the quercetin- and rutin-containing fibrous materials promising candidates for pharmaceutical, cosmetic, and biomedical use.