The electrospinning technique is a commonly employed approach to fabricate fibers intended for various tissue engineering applications. The aim of this study is to develop a novel strategy for tendon repair through the use of aligned poly(ε-caprolactone) (PCL) and poly(glycerol sebacate) (PGS) fibers fabricated in benign solvents, and further explore the potential application of PGS in tendon tissue engineering (TTE). The fibers were characterized for their morphological and physicochemical properties; amniotic epithelial stem cells (AECs) were used to assess the fibers teno-inductive and immunomodulatory potential due to their ability to teno-differentiate undergoing first a stepwise epithelial to mesenchymal transition, and due to their documented therapeutic role in tendon regeneration. The addition of PGS to PCL improved the spinnability of the polymer solution, as well as the uniformity and directionality of the so-obtained fibers. The mechanical properties were in the range of most TTE applications, specifically in the case of PCL/PGS 4:1 and 2:1 ratios. Compared to PCL alone, the same ratios also allowed a better AECs infiltration and growth over 7 days of culture, and triggered the activation of tendon-related genes (SCX, COL1, TNMD) and the expression of tenomodulin (TNMD) at the protein level. Concerning the immunomodulatory properties, both PCL and PCL/PGS fibers negatively affected the immunomodulatory profile of AECs, up-regulating both anti-inflammatory (IL-10) and pro-inflammatory (IL-12) cytokines over 7 days of culture. Overall, PCL/PGS 2:1 fibers fabricated with benign solvents proved to be the most suitable composition for TTE application based on their topographical cues, mechanical properties, biocompatibility, and teno-inductive properties.