In this study, bioactive glass (BG) and copper metal nanoparticles (Cu NPs)-doped poly(epsilon-caprolactone) (PCL) nanofiber membranes were produced by electrospinning method. Box-Behnken design was used to evaluate the effect of formulation variables including PCL concentration, Cu NPs ratio and BG ratio on nanofiber diameter, and cytotoxicity studies on mouse fibroblasts (L-929) were performed to evaluate the formulation suitable for tissue engineering applications. Membranes containing BG showed enhanced cytocompatibility. It was determined that the toxic properties of the membranes increased with the increase of the Cu NPs ratio. In light of these studies, it was determined that 10% w/v PCL concentration, 15% w/w BG ratio and 0.025% w/w Cu NPs ratio were biocompatible with L929 fibroblast cells. The stability and mineralization ability of the obtained membrane in simulated body fluid were determined by scanning electron microscope and X-ray diffraction analysis. This proved the osteogenic potential of the obtained membrane. Copper ions release from the nanofiber mat was detected by inductively coupled plasma-optical emission spectrometry, and it was found that this membrane had an angiogenic potential. Therefore, this study provides an overview of the effect of formulation variables to fabricate PCL nanofiber scaffolds with BG and Cu NPs for tissue engineering applications.