Although the impact of composites based on Ti-doped calcium phosphate glasses is low compared with that of bioglass, they have been already shown to possess great potential for bone tissue engineering. Composites made of polylactic acid (PLA) and a microparticle glass of 5TiO2–44.5CaO–44.5P2O5–6Na2O (G5) molar ratio have already demonstrated in situ osteo- and angiogenesis-triggering abilities. As many of the hybrid materials currently developed usually promote osteogenesis but still lack the ability to induce vascularization, a G5/PLA combination is a cost-effective option for obtaining new instructive scaffolds. In this study, nanostructured PLA-ORMOGLASS (organically modified glass) fibers were produced by electrospinning, in order to fabricate extra-cellular matrix (ECM)-like substrates that simultaneously promote bone formation and vascularization. Physical–chemical and surface characterization and tensile tests demonstrated that the obtained scaffolds exhibited homogeneous morphology, higher hydrophilicity and enhanced mechanical properties than pure PLA. In vitro assays with rat mesenchymal stem cells (rMSCs) and rat endothelial progenitor cells (rEPCs) also showed that rMSCs attached and proliferated on the materials influenced by the calcium content in the environment. In vivo assays showed that hybrid composite PLA-ORMOGLASS fibers were able to promote the formation of blood vessels. Thus, these novel fibers are a valid option for the design of functional materials for tissue engineering applications.