Herein, we report a drug eluting scaffold composed of a composite nanofibers of poly(ε-caprolactone) (PCL) and poly(glycerol sebacate) (PGS) loaded with Hydroxyapatite nanoparticles (HANPs) and simvastatin (SIM) mimicking the bone extracellular matrix (ECM) to improve bone cell proliferation and regeneration process. Indeed, the addition of PGS results in a slight increase in the average fiber diameter compared to PCL. However, the presence of HANPs in the composite nanofibers induced a greater fiber diameter distribution, without significantly changing the average fiber diameter. The in vitro drug release result revealed that the sustained release of SIM from the composite nanofiber obeying the Korsemeyer–Peppas and Kpocha models revealing a non-Fickian diffusion mechanism and the release mechanism follows diffusion rather than polymer erosion. Biomineralization assessment of the nanofibers was carried out in simulated body fluid (SBF). SEM and EDS analysis confirmed nucleation of the hydroxyapatite layer on the surface of the composite nanofibers mimicking the natural apatite layer. Moreover, in vitro studies revealed that the PCL-PGS-HA displayed better cell proliferation and adhesion compared to the control sample, hence improving the regeneration process. This suggests that the fabricated PCL-PGS-HA could be a promising future scaffold for control drug delivery and bone tissue regeneration application.