Increased demand for advanced biomaterials in tissue engineering has driven research to develop innovative solutions based on smart material combinations. Mesoporous bioactive glass nanoparticles (MBGNs) have emerged as attractive materials because of their angiogenic and regenerative properties. This study explores the incorporation of boron-doped mesoporous bioactive glass nanoparticles (B-MBGNs) into poly(ε-caprolactone) (PCL) and poly(propylene succinate--glycerol succinate) (PPSG) fibers to enhance their biodegradation and bioactivity. B-MBGNs were synthesized via a microemulsion-assisted sol-gel method and characterized through morphology, pore size distribution, composition, and surface area. PCL/PPSG nanofibers were fabricated using an alternative combination of solvents, formic acid, and acetic acid. B-MBGNs were incorporated into PCL/PPSG solutions at concentrations of 5, 10, and 15 wt % and electrospun into nanofiber mats under a flow rate of 0.2 mL/h at 22 °C and 40% relative humidity, while the voltage applied at the needle tip was 18 kV and -2 kV at the rotating drum. The addition of 10 wt % of B-MBGNs resulted in nanofibers that exhibited a high degradation rate in PBS with a weight loss of 44% in 30 days, significant hydrophilicity with a contact angle of 33°, and improvements in cell viability tested with normal human dermal fibroblasts (NHDF). In addition, the study highlights the effect of the concentration of B-MBGNs on the morphology of the fibers, which can agglomerate and form undesired beads. Although the particles improved cellular activity, the changes in morphology caused tension points that reduced the elasticity of the fibers. Overall, this work contributes to the innovative use of green polyesters combined with boron ions in electrospun fibrous scaffolds, expanding the opportunities for applications in tissue regeneration, for example, to treat chronic wounds in diabetic patients.